Singular integrals, Herz-type function spaces, and boundary problems / Marius Mitrea, Pedro Takemura.

Format:

Book

Author/Creator:

Mitrea, Marius, Author.

Takemura, Pedro, Author.

Series:

Progress in mathematics (Boston, Mass.) ; 362.

Progress in mathematics ; 362

Language:

English

Subjects (All):

Singular integrals.

Boundary value problems.

Physical Description:

x, 691 pages : illustrations ; 24 cm.

Place of Publication:

Cham : Birkhäuser, [2026]

Summary:

"This monograph presents state-of-the-art results at the intersection of Harmonic Analysis, Functional Analysis, Geometric Measure Theory, and Partial Differential Equations, providing tools for treating elliptic boundary value problems for systems of PDE's in rough domains. Largely self-contained, it develops a comprehensive Calderón-Zygmund theory for singular integral operators on many Herz-type spaces, and their associated Hardy and Sobolev spaces, in the optimal geometric-measure theoretic setting of uniformly rectifiable sets. The present work highlights the effectiveness of boundary layer potential methods as a means of establishing well-posedness results for a wide family of boundary value problems, including Dirichlet, Neumann, Regularity, and Transmission Problems. Graduate students, researchers, and professional mathematicians interested in harmonic analysis and boundary problems will find this monograph a valuable resource in the field."-- Provided by publisher.

Contents:

Introduction

Preliminary Matters

Beurling Algebras

Beurling-Hardy Spaces

Functions of Bounded Central Mean Oscillations

Calderon-Zygmund Theory on Beurling-Hardy Spaces and BCMO_p Spaces

Weakly Elliptic Systems and Layer Potentials on UR Domains

Layer Potentials on Beurling-Hardy Spaces and BCMO_p Spaces

Boundary Value Problems on Beurling-Hardy Spaces and BCMO_p Spaces

Herz Spaces of First Generation

Herz-type Hardy Spaces of First Generation

Functions of (p,q)-Bounded Central Mean Oscillations

Calderon-Zygmund Theory on First-Generation Herz-type Spaces

Herz-Based Sobolev Spaces of First Generation

Layer Potentials on Herz-type Spaces of First Generation and Invertibility Results

Boundary Value Problems on Herz-type Spaces of First Generation

Measure Theoretic Herz Spaces

Calderon-Zygmund Theory on Herz Spaces of Second Generation

Boundary Value Problems on Herz Spaces of Second Generation

Inhomogeneous Herz-type Hardy Spaces of Second Generation

Singular Integral Operators on Herz-type Hardy Spaces of Second Generation

Layer Potentials and Boundary Problems on Herz-type Hardy Spaces of Second Generation

A New Class of Herz-type Spaces, Singular Integrals, and Boundary Problems

Herz Spaces on Bounded Ahlfors Regular Sets

Boundary Value Problems in Domains with Compact Boundary.

Notes:

Includes bibliographical references (pages 675-683) and index.

ISBN:

3032125154

9783032125156

OCLC:

1547124567