Dyadic-Probabilistic Methods in Bilinear Analysis.

Format:

Book

Author/Creator:

Martikainen, Henri.

Contributor:

Vuorinen, Emil.

Series:

Memoirs of the American Mathematical Society

Memoirs of the American Mathematical Society ; v.274

Language:

English

Subjects (All):

Bilinear forms.

Calderón-Zygmund operator.

Dyadic analysis (Social sciences).

Physical Description:

1 online resource (94 pages)

Edition:

1st ed.

Place of Publication:

Providence : American Mathematical Society, 2022.

Summary:

"We demonstrate and develop dyadic-probabilistic methods in connection with non-homogeneous bilinear operators, namely singular integrals and square functions. We develop the full non-homogeneous theory of bilinear singular integrals using a modern point of view. The main result is a new global Tb theorem for Calderon-Zygmund operators in this setting. Our main tools include maximal truncations, adapted Cotlar type inequalities and suppression and big piece methods. While proving our bilinear results we also advance and refine the linear theory of Calderon-Zygmund operators by improving techniques and results. For example, we simplify and make more efficient some non-homogeneous summing arguments appearing in T1 type proofs. As a byproduct, we can manage with ease quite general modulus of continuity in the kernel estimates. Our testing conditions are also quite general by virtue of the big piece method of proof"-- Provided by publisher.

Contents:

Cover

Title page

Chapter 1. Introduction

Chapter 2. Adapted Cotlar type inequality and testing condition for _{ ,♯}

Chapter 3. Suppressed bilinear singular integrals

Chapter 4. The big piece

Chapter 5. End point estimates

Chapter 6. Bilinear good lambda method

Chapter 7. Proof of the main theorem

Chapter 8. Weakening the kernel estimates: modified Dini-condition

Chapter 9. Briefly about square functions

Bibliography

Back Cover.

Adapted Cotlar type inequality and testing condition for Tμ,#

Suppressed bilinear singular integrals

The big piece Tb

End point estimates

Bilinear good lambda method

Proof of the main theorem

Weakening the kernel estimates: modified Dini-condition

Briefly about square functions.

Notes:

Description based on publisher supplied metadata and other sources.

"November 2021. Volume 274."

Includes bibliographical references.

Other Format:

Print version: Martikainen, Henri Dyadic-Probabilistic Methods in Bilinear Analysis

ISBN:

9781470469139

1470469138

OCLC:

1295274074