Zygmund’s Program: Some Partial Solutions

Alexander M. Stokolos

Zygmund’s Program: Some Partial Solutions

Mathematical Sciences

Research output: Contribution to conference › Presentation

Abstract

<div class="line" id="line-15"> We present a simple criterion to decide whether the max-imal function associated with a translation invariant basis of multidi-mensional intervals satis&filig;es a weak type (1, 1) estimate. This allows us to complete Zygmund’s program of the description of the translation invariant bases of multidimensional intervals in the particular case of products of two cubic intervals. As a conjecture, we suggest a more precise version of Zygmund’s program.</div>

Original language	American English
State	Published - May 2006
Event	Ohio State University Seminar - Columbus, OH Duration: May 1 2006 → …

Conference

Conference	Ohio State University Seminar
Period	05/1/06 → …

Disciplines

Mathematics

Keywords

Partial Solutions
Zygmund’s Program

Cite this

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title = "Zygmund{\textquoteright}s Program: Some Partial Solutions",

abstract = " We present a simple criterion to decide whether the max-imal function associated with a translation invariant basis of multidi-mensional intervals satis&filig;es a weak type (1, 1) estimate. This allows us to complete Zygmund’s program of the description of the translation invariant bases of multidimensional intervals in the particular case of products of two cubic intervals. As a conjecture, we suggest a more precise version of Zygmund’s program.",

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AB - We present a simple criterion to decide whether the max-imal function associated with a translation invariant basis of multidi-mensional intervals satis&filig;es a weak type (1, 1) estimate. This allows us to complete Zygmund’s program of the description of the translation invariant bases of multidimensional intervals in the particular case of products of two cubic intervals. As a conjecture, we suggest a more precise version of Zygmund’s program.

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KW - Zygmund’s Program

M3 - Presentation

T2 - Ohio State University Seminar

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