Document Type

Article

Publication Date

2013

Keywords

Anisotropic inhomogeneous symbols, Calderón–Zygmund operators, Anisotropic elementary symbols

Abstract

We introduce a class of pseudodifferential operators in the anisotropic setting induced by an expansive dilation A which generalizes the classical isotropic class Smγ,δ of inhomogeneous symbols. We extend a well-known L 2-boundedness result to the anisotropic class S0δ,δ(A), 0 ≤ δ < 1. As a consequence, we deduce that operators with symbols in the anisotropic class S01,0(A) are bounded on L p spaces, 1 < p < ∞.

Publication Title

Collectanea Mathematica

Volume

64

Issue

2

First Page

155

Last Page

173

DOI

http://dx.doi.org/10.1007/s13348-011-0056-6

Required Publisher's Statement

The final publication is available at Springer via http://dx.doi.org/10.1007/s13348-011-0056-6

Comments

This version is the author's post print.

Subjects - Topical (LCSH)

Pseudodifferential operators; Calderón-Zygmund operator

Genre/Form

articles

Type

Text

Rights

Copying of this document in whole or in part is allowable only for scholarly purposes. It is understood, however, that any copying or publication of this document for commercial purposes, or for financial gain, shall not be allowed without the author’s written permission.

Language

English

Format

application/pdf

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