A two-parameter ``Bergman space'' inequality
Author:
J. Michael Wilson
Journal:
Proc. Amer. Math. Soc. 125 (1997), 755-762
MSC (1991):
Primary 42B25, 42B30, 42C10
DOI:
https://doi.org/10.1090/S0002-9939-97-04039-2
MathSciNet review:
1415376
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Abstract | References | Similar Articles | Additional Information
Abstract: For , define
, where
is a tensor product of one-parameter Haar functions. Let
and
. We prove a sufficient condition, which is close to necessary, on double sequences of weights
and non-negative
, which ensures that the inequality
holds for all . We extend our result to an inequality concerning two-parameter wavelet families.
- [WW] R. L. Wheeden, J. M. Wilson, ``Weighted norm estimates for gradients of half-space extensions,'' Indiana University Math. Journal 44 (1995), 917-969. CMP 96:08
- [W] J. M. Wilson, ``Some two-parameter square function inequalities,'' Indiana University Math. Journal 40 (1991), 419-442. MR 92m:26014
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Additional Information
J. Michael Wilson
Affiliation:
Department of Mathematics, University of Vermont, Burlington, Vermont 05405
DOI:
https://doi.org/10.1090/S0002-9939-97-04039-2
Keywords:
Haar functions,
Littlewood-Paley theory,
wavelets,
Bergman space,
weighted norm inequality
Received by editor(s):
February 7, 1995
Additional Notes:
The author was supported by NSF grant DMS 9401498.
Communicated by:
J. Marshall Ash
Article copyright:
© Copyright 1997
American Mathematical Society