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Author : Yongsheng Han
Release : 1994
Genre : Function spaces
Kind : eBook
Book Rating : 092/5 ( reviews)
Book Synopsis Littlewood-Paley Theory on Spaces of Homogeneous Type and the Classical Function Spaces by : Yongsheng Han
Download or read book Littlewood-Paley Theory on Spaces of Homogeneous Type and the Classical Function Spaces written by Yongsheng Han. This book was released on 1994. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Yongsheng Han
Release : 1994
Genre : Mathematics
Kind : eBook
Book Rating : 925/5 ( reviews)
Book Synopsis Littlewood-Paley Theory on Spaces of Homogeneous Type and the Classical Function Spaces by : Yongsheng Han
Download or read book Littlewood-Paley Theory on Spaces of Homogeneous Type and the Classical Function Spaces written by Yongsheng Han. This book was released on 1994. Available in PDF, EPUB and Kindle. Book excerpt: 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 Calder 'on reproducing formula and use it to extend classical results on atomic decomposition, interpolation, and T1 and Tb theorems. Some new results in the classical setting are also obtained: atomic decompositions with vanishing b-moment, and Littlewood-Paley characterizations of Besov and Triebel-Lizorkin spaces with only half the usual smoothness and cancellation conditions on the approximate identity.
Author : Ioseb Genebashvili
Release : 1997-05-15
Genre : Mathematics
Kind : eBook
Book Rating : 952/5 ( reviews)
Book Synopsis Weight Theory for Integral Transforms on Spaces of Homogeneous Type by : Ioseb Genebashvili
Download or read book Weight Theory for Integral Transforms on Spaces of Homogeneous Type written by Ioseb Genebashvili. This book was released on 1997-05-15. Available in PDF, EPUB and Kindle. Book excerpt: This volume gives an account of the current state of weight theory for integral operators, such as maximal functions, Riesz potential, singular integrals and their generalization in Lorentz and Orlicz spaces. Starting with the crucial concept of a space of homogeneous type, it continues with general criteria for the boundedness of the integral operators considered, then address special settings and applications to classical operators in Euclidean spaces.
Author : Donggao Deng
Release : 2008-11-21
Genre : Mathematics
Kind : eBook
Book Rating : 458/5 ( reviews)
Book Synopsis Harmonic Analysis on Spaces of Homogeneous Type by : Donggao Deng
Download or read book Harmonic Analysis on Spaces of Homogeneous Type written by Donggao Deng. This book was released on 2008-11-21. Available in PDF, EPUB and Kindle. Book excerpt: This book could have been entitled “Analysis and Geometry.” The authors are addressing the following issue: Is it possible to perform some harmonic analysis on a set? Harmonic analysis on groups has a long tradition. Here we are given a metric set X with a (positive) Borel measure ? and we would like to construct some algorithms which in the classical setting rely on the Fourier transformation. Needless to say, the Fourier transformation does not exist on an arbitrary metric set. This endeavor is not a revolution. It is a continuation of a line of research whichwasinitiated,acenturyago,withtwofundamentalpapersthatIwould like to discuss brie?y. The ?rst paper is the doctoral dissertation of Alfred Haar, which was submitted at to University of Gottingen ̈ in July 1907. At that time it was known that the Fourier series expansion of a continuous function may diverge at a given point. Haar wanted to know if this phenomenon happens for every 2 orthonormal basis of L [0,1]. He answered this question by constructing an orthonormal basis (today known as the Haar basis) with the property that the expansion (in this basis) of any continuous function uniformly converges to that function.
Author : Dorina Mitrea
Release : 2023-03-03
Genre : Mathematics
Kind : eBook
Book Rating : 183/5 ( reviews)
Book Synopsis Geometric Harmonic Analysis II by : Dorina Mitrea
Download or read book Geometric Harmonic Analysis II written by Dorina Mitrea. This book was released on 2023-03-03. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is part of a larger program, materializing in five volumes, whose principal aim is to develop tools in Real and Harmonic Analysis, of geometric measure theoretic flavor, capable of treating a broad spectrum of boundary value problems formulated in rather general geometric and analytic settings. Volume II is concerned with function spaces measuring size and/or smoothness, such as Hardy spaces, Besov spaces, Triebel-Lizorkin spaces, Sobolev spaces, Morrey spaces, Morrey-Campanato spaces, spaces of functions of Bounded Mean Oscillations, etc., in general geometric settings. Work here also highlights the close interplay between differentiability properties of functions and singular integral operators. The text is intended for researchers, graduate students, and industry professionals interested in harmonic analysis, functional analysis, geometric measure theory, and function space theory.
