Zygmund's program: some partial solutions

Alexander Stokolos[1]

  • [1] DePaul University, department of mathematical sciences, Chicago, IL 60614 (USA)

Annales de l’institut Fourier (2005)

  • Volume: 55, Issue: 5, page 1439-1453
  • ISSN: 0373-0956

Abstract

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We present a simple criterion to decide whether the maximal function associated with a translation invariant basis of multidimensional intervals satisfies 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.

How to cite

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Stokolos, Alexander. "Zygmund's program: some partial solutions." Annales de l’institut Fourier 55.5 (2005): 1439-1453. <http://eudml.org/doc/116222>.

@article{Stokolos2005,
abstract = {We present a simple criterion to decide whether the maximal function associated with a translation invariant basis of multidimensional intervals satisfies 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.},
affiliation = {DePaul University, department of mathematical sciences, Chicago, IL 60614 (USA)},
author = {Stokolos, Alexander},
journal = {Annales de l’institut Fourier},
keywords = {covering lemmas; maximal functions; -class; weak-type estimates},
language = {eng},
number = {5},
pages = {1439-1453},
publisher = {Association des Annales de l'Institut Fourier},
title = {Zygmund's program: some partial solutions},
url = {http://eudml.org/doc/116222},
volume = {55},
year = {2005},
}

TY - JOUR
AU - Stokolos, Alexander
TI - Zygmund's program: some partial solutions
JO - Annales de l’institut Fourier
PY - 2005
PB - Association des Annales de l'Institut Fourier
VL - 55
IS - 5
SP - 1439
EP - 1453
AB - We present a simple criterion to decide whether the maximal function associated with a translation invariant basis of multidimensional intervals satisfies 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.
LA - eng
KW - covering lemmas; maximal functions; -class; weak-type estimates
UR - http://eudml.org/doc/116222
ER -

References

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