Fourier transform of characteristic functions and Lebesgue constants for multiple Fourier series
Localization and Convergence of Eigenfunction Expansions.
Fourier transform, oscillatory multipliers and evolution equations in rearrangement invariant function spaces
Decay of Fourier transforms and summability of eigenfunction expansions
Is an operator on weak which commutes with translations a convolution ?
Estimates of BMO type for singular integrals on spaces of homogeneous type and applications to hypoelliptic PDEs.
Average decay of Fourier transforms and geometry of convex sets.
Let B be a convex body in R, with piecewise smooth boundary and let ^χ denote the Fourier transform of its characteristic function. In this paper we determine the admissible decays of the spherical L averages of ^χ and we relate our analysis to a problem in the geometry of convex sets. As an application we obtain sharp results on the average number of integer lattice points in large bodies randomly positioned in the plane.
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