L(P) ESTIMATES FOR OPERATORS ASSOCIATED TO FLAT CURVES WITHOUT THE FOURIER-TRANSFORM

Authors
CARBERY A VANCE J WAINGER S WATSON D WRIGHT J
Citation
A. Carbery et al., L(P) ESTIMATES FOR OPERATORS ASSOCIATED TO FLAT CURVES WITHOUT THE FOURIER-TRANSFORM, Pacific journal of mathematics, 167(2), 1995, pp. 243-262
Citations number
11
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Pacific journal of mathematics → ACNP
ISSN journal
00308730
Volume
167
Issue
2
Year of publication
1995
Pages
243 - 262
Database
ISI
SICI code
0030-8730(1995)167:2<243:LEFOAT>2.0.ZU;2-N
Abstract
The purpose of this paper is to provide new proofs to known theorems o n the L(p) boundedness of the maximal function and Hilbert transform c orresponding to curves in R(n) which are ''infinitely flat'' at the or igin. The old proofs use the Fourier transform in a crucial way. The p resent proofs avoid the Fourier transform and hence at least have the potential of being used in more general situations.