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Wave front sets, local smoothing and Bourgain’s circular maximal theorem. (English) Zbl 0759.42016

The authors consider the maximal operators associated with circular means in two dimensions and their corresponding maximal operators. They obtain a new proof of Bourgain’s circular maximal theorem [cf. J. Bourgain, J. Anal. Mat. 47, 69-85 (1986; Zbl 0626.42012)] as well as a sharpening of known regularity results for the wave equation.

MSC:

42B25 Maximal functions, Littlewood-Paley theory
42B15 Multipliers for harmonic analysis in several variables
42B20 Singular and oscillatory integrals (Calderón-Zygmund, etc.)
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation

Citations:

Zbl 0626.42012
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