A generalization of Bourgain’s circular maximal theorem

Wilhelm Schlag

Type: Article

Publication Date: 1997-01-01

Citations: 76

DOI: https://doi.org/10.1090/s0894-0347-97-00217-8

Abstract

where dσr is the normalized surface measure on r S1. It is easy to see that M is not bounded on L2 (see Example 1.1 below). A well-known result of Bourgain [1] asserts that M is bounded on Lp for 2 < p ≤ ∞. We will consider the question of boundedness of M and Mδ from Lp to Lq. Unless stated to the contrary, we will be dealing only with functions defined on R2. Absolute constants will be denoted by C, and the notation ??? will mean = up to a constant.

Locations

Journal of the American Mathematical Society - View - PDF

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+ PDF Chat	Oscillatory integrals and multiplier problem for the disc	1972	Lennart Carleson Per Sjölin
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