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Theory of Function Spaces II
117,69 € *
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Theory of Function Spaces II deals with the theory of function spaces of type Bspq and Fspq as it stands at the present. These two scales of spaces cover many well-known function spaces such as Hölder-Zygmund spaces, (fractional) Sobolev spaces, Besov spaces, inhomogeneous Hardy spaces, spaces of BMO-type and local approximation spaces which are closely connected with Morrey-Campanato spaces.Theory of Function Spaces II is self-contained, although it may be considered an update of the author's earlier book of the same title.The book's 7 chapters start with a historical survey of the subject, and then analyze the theory of function spaces in Rn and in domains, applications to (exotic) pseudo-differential operators, and function spaces on Riemannian manifolds.------ ReviewsThe first chapter deserves special attention. This chapter is both an outstanding historical survey of function spaces treated in the book and a remarkable survey of rather different techniques developed in the last 50 years. It is shown that all these apparently different methods are only different ways of characterizing the same classes of functions. The book can be best recommended to researchers and advanced students working on functional analysis.- Zentralblatt MATH

Anbieter: Dodax
Stand: 21.10.2020
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Multi-Layer Potentials and Boundary Problems
69,54 € *
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Many phenomena in engineering and mathematical physics can be modeled by means of boundary value problems for a certain elliptic differential operator in a given domain. When the differential operator under discussion is of second order a variety of tools are available for dealing with such problems, including boundary integral methods, variational methods, harmonic measure techniques, and methods based on classical harmonic analysis. When the differential operator is of higher-order (as is the case, e.g., with anisotropic plate bending when one deals with a fourth order operator) only a few options could be successfully implemented. In the 1970s Alberto Calderón, one of the founders of the modern theory of Singular Integral Operators, advocated the use of layer potentials for the treatment of higher-order elliptic boundary value problems. The present monograph represents the first systematic treatment based on this approach.This research monograph lays, for the first time, the mathematical foundation aimed at solving boundary value problems for higher-order elliptic operators in non-smooth domains using the layer potential method and addresses a comprehensive range of topics, dealing with elliptic boundary value problems in non-smooth domains including layer potentials, jump relations, non-tangential maximal function estimates, multi-traces and extensions, boundary value problems with data in Whitney-Lebesque spaces, Whitney-Besov spaces, Whitney-Sobolev- based Lebesgue spaces, Whitney-Triebel-Lizorkin spaces,Whitney-Sobolev-based Hardy spaces, Whitney-BMO and Whitney-VMO spaces.

Anbieter: Dodax
Stand: 21.10.2020
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Inequalities for Differential Forms
129,84 € *
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This monograph is the first one to systematically present a series of local and global estimates and inequalities for differential forms, in particular the ones that satisfy the A-harmonic equations. The presentation focuses on the Hardy-Littlewood, Poincare, Cacciooli, imbedded and reverse Holder inequalities. Integral estimates for operators, such as homotopy operator, the Laplace-Beltrami operator, and the gradient operator are discussed next. Additionally, some related topics such as BMO inequalities, Lipschitz classes, Orlicz spaces and inequalities in Carnot groups are discussed in the concluding chapter. An abundance of bibliographical references and historical material supplement the text throughout.This rigorous presentation requires a familiarity with topics such as differential forms, topology and Sobolev space theory. It will serve as an invaluable reference for researchers, instructors and graduate students in analysis and partial differential equations and could be used as additional material for specific courses in these fields.

Anbieter: Dodax
Stand: 21.10.2020
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Theory of Function Spaces II
92,90 CHF *
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Theory of Function Spaces II deals with the theory of function spaces of type Bspq and Fspq as it stands at the present. These two scales of spaces cover many well-known function spaces such as Hölder-Zygmund spaces, (fractional) Sobolev spaces, Besov spaces, inhomogeneous Hardy spaces, spaces of BMO-type and local approximation spaces which are closely connected with Morrey-Campanato spaces. Theory of Function Spaces II is self-contained, although it may be considered an update of the author’s earlier book of the same title. The book’s 7 chapters start with a historical survey of the subject, and then analyze the theory of function spaces in Rn and in domains, applications to (exotic) pseudo-differential operators, and function spaces on Riemannian manifolds. ------ Reviews The first chapter deserves special attention. This chapter is both an outstanding historical survey of function spaces treated in the book and a remarkable survey of rather different techniques developed in the last 50 years. It is shown that all these apparently different methods are only different ways of characterizing the same classes of functions. The book can be best recommended to researchers and advanced students working on functional analysis. - Zentralblatt MATH

Anbieter: Orell Fuessli CH
Stand: 21.10.2020
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Hardy Spaces on the Euclidean Space
155,00 CHF *
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'Still waters run deep.' This proverb expresses exactly how a mathematician Akihito Uchiyama and his works were. He was not celebrated except in the field of harmonic analysis, and indeed he never wanted that. He suddenly passed away in summer of 1997 at the age of 48. However, nowadays his contributions to the fields of harmonic analysis and real analysis are permeating through various fields of analysis deep and wide. One could write several papers explaining his contributions and how they have been absorbed into these fields, developed, and used in further breakthroughs. Peter W. Jones (Professor of Yale University) says in his special contribution to this book that Uchiyama's decomposition of BMO functions is considered to be the Mount Everest of Hardy space theory. This book is based on the draft, which the author Akihito Uchiyama had completed by 1990. It deals with the theory of real Hardy spaces on the n-dimensional Euclidean space. Here the author explains scrupulously some of important results on Hardy spaces by real-variable methods, in particular, the atomic decomposition of elements in Hardy spaces and his constructive proof of the Fefferman-Stein decomposition of BMO functions into the sum of a bounded?function and Riesz transforms of bounded functions.

Anbieter: Orell Fuessli CH
Stand: 21.10.2020
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Séminaire de Probabilités XIII
69,90 CHF *
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On the integrability of Banach space valued Walsh polynomials.- Le principe de sous-suites dans les espaces de Banach.- Domains of attraction in Banach spaces.- Charges, poids et mesures de Levy dans les espaces vectoriels localement convexes.- Random fourier series on locally compact abelian groups.- Une solution simple au probleme de Skorokhod.- Demonstration elementaire d'un resultat d'Azema et Jeulin.- Sauts additifs et sauts multiplicatifs des semi-martingales.- Le support exact du temps local d'une martingale continue.- Martingales locales a accroissements independants.- Decomposition de martingales locales et rarefaction des sauts.- Un critere previsible pour l'uniforme integrabilite des semimartingales exponentielles.- Sur la convergence des martingales indexees par ? ¿?.- Arret de certaines suites multiples de variables aleatoires independantes.- Une remarque sur le calcul stochastique dependant d'un parametre.- Quasimartingales et formes lineaires associees.- Sur la p-variation d'une surmartingale continue.- Sur la p-variation des surmartingales.- Une remarque sur l'expose precedent.- Representations multiplicatives de sousmartingales.- Caracterisation d'une classe de semimartingales.- Sur les integrales stochastiques de L.C. Young.- Une topologie sur l'espace des semimartingales.- Equations differentielles lipschitziennes etude de la stabilite.- Fonction maximale et variation quadratique des martingales en presence d'un poids.- Weighted norm inequalities for martingales.- Inegalites de normes avec poids.- In¿lit¿e Hardy, semimartingales, et faux-amis.- Sur l'expression de la dualit¿ntre H1 et BMO.- Inegalites de convexite pour les processus croissants et les sousmartingales.- Theoreme de separation dans le probleme d'arret optimal.- Martingales et changements de temps.- Quelques epilogues.- En cherchant une d¿nition naturelle des int¿ales stochastiques optionnelles.- Les filtrations de certaines martingales du mouvement brownien dans ?n.- Demonstration simple d'un resultat sur le temps local.- Temps local et balayage des semi-martingales.- Sur le balayage des semi-martingales continues.- Semimartingales et valeur absolue.- Sur une formule de la theorie du balayage.- Construction de quasimartingales s'annulant sur un ensemble donne.- Conditional excursion theory.- Problemes a frontiere libre et arbres de mesures.- Un th¿¿ de J.W. Pitman.- Mesures de probabilite sur les entiers et ensembles Progressions.- On the uniqueness of optimal controls.- Processus de diffusion gouverne par la forme de dirichlet de l'operateur de Schr¿dinger.- Operateur de Schr¿dinger a resolvante compacte.- Grossissement d'une filtration et applications.- Encore une remarque sur la ? formule de balayage ?.- Presentation de l'?inegalite de doob ? de metivier-pellaumail.- Solution explicite de l'equation .- Caracterisation des semimartingales, d'apres dellacherie.- Un exemple de J. Pitman.- Le probleme de skorokhod : complements a l'expose precedent.- A propos de la formule d'Azema-Yor.- Martingales de valeur absolue donnee, d'apres Protter et Sharpe.- On the left end points of Brownian excursions.

Anbieter: Orell Fuessli CH
Stand: 21.10.2020
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Brownian Motion, Hardy Spaces and Bounded Mean ...
37,90 CHF *
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This exposition of research on the martingale and analytic inequalities associated with Hardy spaces and functions of bounded mean oscillation (BMO) introduces the subject by concentrating on the connection between the probabilistic and analytic approaches. Short surveys of classical results on the maximal, square and Littlewood-Paley functions and the theory of Brownian motion introduce a detailed discussion of the Burkholder-Gundy-Silverstein characterization of HP in terms of maximal functions. The book examines the basis of the abstract martingale definitions of HP and BMO, makes generally available for the first time work of Gundy et al. on characterizations of BMO, and includes a probabilistic proof of the Fefferman-Stein Theorem on the duality of H11 and BMO.

Anbieter: Orell Fuessli CH
Stand: 21.10.2020
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Inequalities for Differential Forms
162,90 CHF *
ggf. zzgl. Versand

This monograph is the first one to systematically present a series of local and global estimates and inequalities for differential forms, in particular the ones that satisfy the A-harmonic equations. The presentation focuses on the Hardy-Littlewood, Poincare, Cacciooli, imbedded and reverse Holder inequalities. Integral estimates for operators, such as homotopy operator, the Laplace-Beltrami operator, and the gradient operator are discussed next. Additionally, some related topics such as BMO inequalities, Lipschitz classes, Orlicz spaces and inequalities in Carnot groups are discussed in the concluding chapter. An abundance of bibliographical references and historical material supplement the text throughout. This rigorous presentation requires a familiarity with topics such as differential forms, topology and Sobolev space theory. It will serve as an invaluable reference for researchers, instructors and graduate students in analysis and partial differential equations and could be used as additional material for specific courses in these fields.

Anbieter: Orell Fuessli CH
Stand: 21.10.2020
Zum Angebot
Mean Oscillations and Equimeasurable Rearrangem...
53,90 CHF *
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Various applications of equimeasurable function rearrangements to the 'best constant'-type problems are considered in this volume. Several classical theorems are presented along with some very recent results. In particular, the text includes a product-space extension of the Rising Sun lemma, a product-space version of the John-Nirenberg inequality for bounded mean oscillation (BMO) functions with sharp exponent, a refinement of the Gurov-Reshetnyak lemma, sharp embedding theorems for Muckenhoupt, Gurov-Reshetnyak, reverse Hölder, and Gehring classes, etc. This volume is interesting for graduate students and mathematicians involved with these topics. TOC:Preface.- 1.Preliminaries and auxilliary results.- 2. Properties of oscillations and the definition of the BMO-class.- 3.Estimates of rearrangements and the John-Nirenberg theorem.- 4.The BMO-estimates of the Hardy-type transforms.- 5.The Gurov-Reshetnyak class of functions.- Appendix: A.The boundedness of the Hardy-Littlewood maximal operator from BMO into BLO.- B.The weighted analogs of the Riesz lemma and the Gurov-Reshetnyak theorem.- C.Classes of functions satisfying the reverse Hölder inequality.- References.- Index.

Anbieter: Orell Fuessli CH
Stand: 21.10.2020
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