Hardy Spaces of Exact Forms on Domains
Author | : Zengjian Lou |
Publisher | : |
Total Pages | : 228 |
Release | : 2002 |
Genre | : Function spaces |
ISBN | : |
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Author | : Zengjian Lou |
Publisher | : |
Total Pages | : 228 |
Release | : 2002 |
Genre | : Function spaces |
ISBN | : |
Author | : Alexandru Aleman |
Publisher | : Springer Science & Business Media |
Total Pages | : 135 |
Release | : 2010-01-08 |
Genre | : Mathematics |
ISBN | : 3034600984 |
If H is a Hilbert space and T : H ? H is a continous linear operator, a natural question to ask is: What are the closed subspaces M of H for which T M ? M? Of course the famous invariant subspace problem asks whether or not T has any non-trivial invariant subspaces. This monograph is part of a long line of study of the invariant subspaces of the operator T = M (multiplication by the independent variable z, i. e. , M f = zf )on a z z Hilbert space of analytic functions on a bounded domain G in C. The characterization of these M -invariant subspaces is particularly interesting since it entails both the properties z of the functions inside the domain G, their zero sets for example, as well as the behavior of the functions near the boundary of G. The operator M is not only interesting in its z own right but often serves as a model operator for certain classes of linear operators. By this we mean that given an operator T on H with certain properties (certain subnormal operators or two-isometric operators with the right spectral properties, etc. ), there is a Hilbert space of analytic functions on a domain G for which T is unitarity equivalent to M .
Author | : Javad Mashreghi |
Publisher | : American Mathematical Soc. |
Total Pages | : 230 |
Release | : 2010-01-01 |
Genre | : Mathematics |
ISBN | : 0821870459 |
Author | : Irene Sabadini |
Publisher | : Springer Science & Business Media |
Total Pages | : 172 |
Release | : 2008-12-16 |
Genre | : Mathematics |
ISBN | : 0817644164 |
* Original articles and survey articles in honor of the sixtieth birthday of Carlos A. Berenstein reflect his diverse research interests from interpolation to residue theory to deconvolution and its applications to issues ranging from optics to the study of blood flow * Contains both theoretical papers in harmonic and complex analysis, as well as more applied work in signal processing * Top-notch contributors in their respective fields
Author | : Yuefei Wang |
Publisher | : World Scientific |
Total Pages | : 349 |
Release | : 2006 |
Genre | : Mathematics |
ISBN | : 9812568689 |
This valuable collection of articles presents the latest methods and results in complex analysis and its applications. The present trends in complex analysis reflected in the book are concentrated in the following research directions: Clifford analysis, complex dynamical systems, complex function spaces, complex numerical analysis, qusiconformal mapping, Riemann surfaces, Teichmller theory and Klainian groups, several complex variables, and value distribution theory.
Author | : Ravi P. Agarwal |
Publisher | : Springer Science & Business Media |
Total Pages | : 392 |
Release | : 2009-09-19 |
Genre | : Mathematics |
ISBN | : 0387684174 |
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.
Author | : Steve Hofmann |
Publisher | : American Mathematical Soc. |
Total Pages | : 91 |
Release | : 2011 |
Genre | : Mathematics |
ISBN | : 0821852388 |
Let $X$ be a metric space with doubling measure, and $L$ be a non-negative, self-adjoint operator satisfying Davies-Gaffney bounds on $L^2(X)$. In this article the authors present a theory of Hardy and BMO spaces associated to $L$, including an atomic (or molecular) decomposition, square function characterization, and duality of Hardy and BMO spaces. Further specializing to the case that $L$ is a Schrodinger operator on $\mathbb{R}^n$ with a non-negative, locally integrable potential, the authors establish additional characterizations of such Hardy spaces in terms of maximal functions. Finally, they define Hardy spaces $H^p_L(X)$ for $p>1$, which may or may not coincide with the space $L^p(X)$, and show that they interpolate with $H^1_L(X)$ spaces by the complex method.
Author | : Tadeusz Iwaniec |
Publisher | : American Mathematical Soc. |
Total Pages | : 110 |
Release | : 2008 |
Genre | : Mathematics |
ISBN | : 0821840452 |
The measurable Riemann Mapping Theorem (or the existence theorem for quasiconformal mappings) has found a central role in a diverse variety of areas such as holomorphic dynamics, Teichmuller theory, low dimensional topology and geometry, and the planar theory of PDEs. Anticipating the needs of future researchers, the authors give an account of the state of the art as it pertains to this theorem, that is, to the existence and uniqueness theory of the planar Beltrami equation, and various properties of the solutions to this equation. The classical theory concerns itself with the uniformly elliptic case (quasiconformal mappings). Here the authors develop the theory in the more general framework of mappings of finite distortion and the associated degenerate elliptic equations.
Author | : Nikolaï Nikolski |
Publisher | : Cambridge University Press |
Total Pages | : 297 |
Release | : 2019-01-31 |
Genre | : Mathematics |
ISBN | : 1107184541 |
Graduate text covering the theory of Hardy spaces from its origins to the present, with concrete applications and solved exercises.
Author | : Martin Dindoš |
Publisher | : |
Total Pages | : 92 |
Release | : 2014-09-11 |
Genre | : Hardy spaces |
ISBN | : 9781470405007 |
Studies Hardy spaces on $C DEGREES1$ and Lipschitz domains in Riemannian manifolds. The author establishes this theorem in any dimension if the domain is $C DEGREES1$, in case of a Lipschitz domain the result holds if dim $M\le 3$. The remaining cases for Lipschitz domain