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

Mockenhaupt, Gerd; Seeger, Andreas; Sogge, Christopher D.

Ann. Math. (2) 136, No. 1, 207-218 (1992).

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.

Reviewer: M.Milman (Boca Raton)

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

Keywords:

maximal operators; circular means; Bourgain’s circular maximal theorem; regularity; wave equation

Citations:

Zbl 0626.42012