Distribution function inequalities for the density of the area integral

R. Banuelos; C. N. Moore

Annales de l'institut Fourier (1991)

  • Volume: 41, Issue: 1, page 137-171
  • ISSN: 0373-0956

Abstract

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We prove good- λ inequalities for the area integral, the nontangential maximal function, and the maximal density of the area integral. This answers a question raised by R. F. Gundy. We also prove a Kesten type law of the iterated logarithm for harmonic functions. Our Theorems 1 and 2 are for Lipschitz domains. However, all our results are new even in the case of R + 2 .

How to cite

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Banuelos, R., and Moore, C. N.. "Distribution function inequalities for the density of the area integral." Annales de l'institut Fourier 41.1 (1991): 137-171. <http://eudml.org/doc/74911>.

@article{Banuelos1991,
abstract = {We prove good-$\lambda $ inequalities for the area integral, the nontangential maximal function, and the maximal density of the area integral. This answers a question raised by R. F. Gundy. We also prove a Kesten type law of the iterated logarithm for harmonic functions. Our Theorems 1 and 2 are for Lipschitz domains. However, all our results are new even in the case of $\{\{\bf R\}\}^ 2_+$.},
author = {Banuelos, R., Moore, C. N.},
journal = {Annales de l'institut Fourier},
keywords = {distribution function inequalities; local time; good- inequalities; area integral; nontangential; maximal function; maximal density; iterated logarithm for harmonic functions},
language = {eng},
number = {1},
pages = {137-171},
publisher = {Association des Annales de l'Institut Fourier},
title = {Distribution function inequalities for the density of the area integral},
url = {http://eudml.org/doc/74911},
volume = {41},
year = {1991},
}

TY - JOUR
AU - Banuelos, R.
AU - Moore, C. N.
TI - Distribution function inequalities for the density of the area integral
JO - Annales de l'institut Fourier
PY - 1991
PB - Association des Annales de l'Institut Fourier
VL - 41
IS - 1
SP - 137
EP - 171
AB - We prove good-$\lambda $ inequalities for the area integral, the nontangential maximal function, and the maximal density of the area integral. This answers a question raised by R. F. Gundy. We also prove a Kesten type law of the iterated logarithm for harmonic functions. Our Theorems 1 and 2 are for Lipschitz domains. However, all our results are new even in the case of ${{\bf R}}^ 2_+$.
LA - eng
KW - distribution function inequalities; local time; good- inequalities; area integral; nontangential; maximal function; maximal density; iterated logarithm for harmonic functions
UR - http://eudml.org/doc/74911
ER -

References

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