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Geometric harmonic analysis.II,Function spaces measuring size and smoothness on rough sets

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Geometric harmonic analysis.by Dorina Mitrea, Irina Mitrea, Marius Mitrea.
其他題名:	Function spaces measuring size and smoothness on rough sets
作者:	Mitrea, Dorina.
其他作者:	Mitrea, Irina.
出版者:	Cham :Springer International Publishing :2022.
面頁冊數:	xix, 930 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Harmonic analysis.
電子資源:	https://doi.org/10.1007/978-3-031-13718-1
ISBN:	9783031137181$q(electronic bk.)

Geometric harmonic analysis.II,Function spaces measuring size and smoothness on rough sets
Mitrea, Dorina.

Geometric harmonic analysis.II,Function spaces measuring size and smoothness on rough sets[electronic resource] /Function spaces measuring size and smoothness on rough setsby Dorina Mitrea, Irina Mitrea, Marius Mitrea. - Cham :Springer International Publishing :2022. - xix, 930 p. :ill., digital ;24 cm. - Developments in mathematics,v. 732197-795X ;. - Developments in mathematics ;v.25..

1 Preliminary Functional Analytic Matters -- 2 Abstract Fredholm Theory -- 3 Functions of Vanishing Mean Oscillations and Vanishing Hölder Moduli -- 4 Hardy Spaces on Ahlfors Regular Sets -- 5 Banach Function Spaces, Extrapolation, and Orlicz Spaces -- 6 Morrey-Campanato Spaces, Morrey Spaces, and Their Pre-Duals on Ahlfors Regular Sets -- 7 Besov and Triebel-Lizorkin Spaces on Ahlfors Regular Sets -- 8 Boundary Traces from Weighted Sobolev Spaces into Besov Spaces -- 9 Besov and Triebel-Lizorkin Spaces in Open Sets -- 10 Strong and Weak Normal Boundary Traces of Vector Fields in Hardy and Morrey Spaces -- 11 Sobolev Spaces on the Geometric Measure Theoretic Boundary of Sets of Locally Finite Perimeter -- A. Terms and Notation Used in Volume II. References -- Index.

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.

ISBN: 9783031137181$q(electronic bk.)

Standard No.: 10.1007/978-3-031-13718-1doiSubjects--Topical Terms:

189705
Harmonic analysis.

LC Class. No.: QA403

Dewey Class. No.: 515.2433

Geometric harmonic analysis.II,Function spaces measuring size and smoothness on rough sets
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505 0 $a 1 Preliminary Functional Analytic Matters -- 2 Abstract Fredholm Theory -- 3 Functions of Vanishing Mean Oscillations and Vanishing Hölder Moduli -- 4 Hardy Spaces on Ahlfors Regular Sets -- 5 Banach Function Spaces, Extrapolation, and Orlicz Spaces -- 6 Morrey-Campanato Spaces, Morrey Spaces, and Their Pre-Duals on Ahlfors Regular Sets -- 7 Besov and Triebel-Lizorkin Spaces on Ahlfors Regular Sets -- 8 Boundary Traces from Weighted Sobolev Spaces into Besov Spaces -- 9 Besov and Triebel-Lizorkin Spaces in Open Sets -- 10 Strong and Weak Normal Boundary Traces of Vector Fields in Hardy and Morrey Spaces -- 11 Sobolev Spaces on the Geometric Measure Theoretic Boundary of Sets of Locally Finite Perimeter -- A. Terms and Notation Used in Volume II. References -- Index.
520 $a 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.
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