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Hardy Operators, Function Spaces and Embeddings
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David E Edmunds, W Desmond Evans
Classical Sobolev spaces, based on Lebesgue spaces on an underlying domain with smooth boundary, are not only of considerable intrinsic interest but have for many years proved to be indispensible in the study of partial differential equations and variational problems. Many developments of the basic theory since its inception arise in response to ...
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An Introduction to Operators on the Hardy-Hilbert Space
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Peter Rosenthal, Ruben A Martinez-Avendano, Rubn A Martinez-Avendano
The subject of this book is operator theory on the Hardy space H2, also called the Hardy-Hilbert space. This is a popular area, partially because the Hardy-Hilbert space is the most natural setting for operator theory. A reader who masters the material covered in this book will have acquired a firm foundation for the study of all spaces of ...
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Brownian Motion, Hardy Spaces and Bounded Mean Oscillation
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Karl Endel Petersen, J W S Cassels (Editor), N J Hitchin (Editor)
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 ...
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Introduction to HP Spaces
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Paul Koosis
In this book, the author shows how, from simple ideas, one can build up an investigation that explains and clarifies many different, seemingly unrelated problems; to show, in effect, how mathematics grows. Researchers in analysis and probability will find this title of interest.
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Function Theory on Planar Domains: A Second Course in Complex Analysis
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Stephen D Fisher
Suitable for upper-level undergraduates and graduate students, this treatment of complex analysis focuses on function theory on a finitely connected planar domain. Clear and complete, it emphasizes domains bounded by a finite number of disjoint analytic simple closed curves. The author is Professor of Mathematics at Northwestern University. 1983 ...
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Clifford Wavelets, Singular Integrals, and Hardy Spaces
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by
Marius Mitrea
This monograph discusses the extensions of basic Fourier analysis to the Clifford algebra framework. Topics covered include: construction of Clifford-valued wavelets; Calderon-Zygmund theory for Clifford valued singular integral operators on Lipschitz hyper-surfaces; and Hardy spaces of Clifford monogenic functions on Lipschitz domains. Results ...
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Summability of Multi-Dimensional Fourier Series and Hardy Spaces
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Ferenc Weisz, Ferenc Weiz
This is the first monograph which considers the theory of more-parameter dyadic and classical Hardy spaces. In this book, a new application of martingale and distribution theories is dealt with. The theories of the multi-parameter dyadic martingale and the classical Hardy spaces are applied in Fourier analysis. Several summability methods of d ...
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Weighted Hardy Spaces
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Jan-Olov Strmberg, Alberto Torchinsky, Jan-Olov Stramberg
These notes give the basic ingredients of the theory of weighted Hardy spaces of tempered distribution on Rn and illustrate the techniques used. The authors consider properties of weights in a general setting; they derive mean value inequalities for wavelet transforms and introduce halfspace techniques with, for example, nontangential maximal ...
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Theory of Hp spaces
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Peter L Duren
A blend of classical and modern techniques and viewpoints, this text examines harmonic and subharmonic functions, the basic structure of Hp functions, applications, Taylor coefficients, interpolation theory, more. 1970 edition.
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Hardy Spaces on Homogeneous Groups. (MN-28)
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Elias M Stein, Gerald B Folland
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Nonlinear commutators in interpolation theory
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Nigel J. Kalton
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Four Lectures on Real HP Space
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Shanzhen Lu
This text examines the real variable theory of HP spaces, concentrating on its applications to various aspects of analysis fields.
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Hardy Spaces and Potential Theory on C[superscript 1] Domains in Riemannian Manifolds
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by
Martin Dindo's
The author studies Hardy spaces on $C1$ and Lipschitz domains in Riemannian manifolds. Hardy spaces, originally introduced in 1920 in complex analysis setting, are invaluable tool in harmonic analysis. For this reason these spaces have been studied extensively by many authors.
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Hardy Spaces on the Euclidean Space
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by
Akihito Uchiyama
Still waters run deep.
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Littlewood-Paley Theory on Spaces of Homogeneous Type and the Classical Function Spaces
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by
Yongsheng Han
In this work, Han and Sawyer extend Littlewood-Paley theory, Besov spaces, and Triebel-Lizorkin spaces to the general setting of a space of homogeneous type. For this purpose, they establish a suitable analogue of the Calderon reproducing formula and use it to extend classical results on atomic decomposition, interpolation, and T1 and Tb theorems. ...
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The Backward Shift on the Hardy Space
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by
Joseph A Cima
Shift operators on Hilbert spaces of analytic functions play an important role in the study of bounded linear operators on Hilbert spaces since they often serve as models for various classes of linear operators. For example, 'parts' of direct sums of the backward shift operator on the classical Hardy space H2 model certain types of contraction ...
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Embedding and Multiplier Theorems for H(superscript P)(R(superscript N))
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A. Baernstein, E. T. Sawyer
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Weighted Hardy Spaces
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Jan-Olov Stromberg
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Sub-Hardy Hilbert Spaces in the Unit Disk
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by
Donald Sarason
Originally developed in 1966, Hilbert spaces have undergone intense investigation in the past few years. This book concerns a family of Hilbert spaces of holomorphic functions in the unit disk. Besides possessing a fascinating internal structure, they play a role in several basic problems in function theory. This book develops the basic structure ...
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Introduction to HP Spaces, with an Appendix on Wolff's Proof of the Corona Theorem
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by
Paul Koosis
In this book, the author shows how, from simple ideas, one can build up an investigation that explains and clarifies many different, seemingly unrelated problems; to show, in effect, how mathematics grows. Researchers in analysis and probability will find this title of interest.
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Abstract Analytic Function Theory and Hardy Algebras
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Klaus Barbey
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Martingale Hardy spaces and their applications in Fourier analysis
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Weisz
This monograph deals with the theory of one-and two-parameter martingale Hardy spaces and their use in Fourier analysis. The atomic decomposition method is applied to both theories, and a new proof of Carleson's convergence result, using martingale methods, is provided.
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Operator Valued Hardy Spaces
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by
Tao Mei
The author gives a systematic study of the Hardy spaces of functions with values in the noncommutative $Lp$-spaces associated with a semifinite von Neumann algebra $\mathcal{M .$ This is motivated by matrix valued Harmonic Analysis (operator weighted norm inequalities, operator Hilbert transform), as well as by the recent development of ...
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Anisotropic Hardy Spaces and Wavelets
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by
Marcin Bownik
In this paper, motivated in part by the role of discrete groups of dilations in wavelet theory, we introduce and investigate the anisotropic Hardy spaces associated with very general discrete groups of dilations. This formulation includes the classical isotropic Hardy space theory of Fefferman and Stein and parabolic Hardy space theory of Calderon ...
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Theory of H[superscript p] spaces
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Peter L. Duren
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