Approximation of Lebesgue Integrals by Riemann Sums and Lattice Points in Domains with Fractal Boundary.
Hankel transform on Lorentz spaces
Translation invariant operators on Lorentz spaces
Localization and Convergence of Eigenfunction Expansions.
Fourier transform, oscillatory multipliers and evolution equations in rearrangement invariant function spaces
Translation-invariant operators on Lorentz spaces L(1,q) with 0 < q < 1
We study convolution operators bounded on the non-normable Lorentz spaces of the real line and the torus. Here 0 < q < 1. On the real line, such an operator is given by convolution with a discrete measure, but on the torus a convolutor can also be an integrable function. We then give some necessary and some sufficient conditions for a measure or a function to be a convolutor on . In particular, when the positions of the atoms of a discrete measure are linearly independent over the rationals,...
Hardy-Lorentz spaces and expansions in eigenfunctions of the Laplace-Beltrami operator on compact manifolds
Decay of Fourier transforms and summability of eigenfunction expansions
Is an operator on weak which commutes with translations a convolution ?
Eigenfunctions of the Hardy-Littlewood maximal operator
We prove that peak shaped eigenfunctions of the one-dimensional uncentered Hardy-Littlewood maximal operator are symmetric and homogeneous. This implies that the norms of the maximal operator on L(p) spaces are not attained.
From restricted type to strong type estimates on quasi-Banach rearrangement invariant spaces
Let X be a quasi-Banach rearrangement invariant space and let T be an (ε,δ)-atomic operator for which a restricted type estimate of the form for some positive function D and every measurable set E is known. We show that this estimate can be extended to the set of all positive functions f ∈ L¹ such that , in the sense that . This inequality allows us to obtain strong type estimates for T on several classes of spaces as soon as some information about the galb of the space X is known. In this paper...
Pointwise convergence of Fourier series on compact Lie groups
Sharp results for the mean summability of Fourier series on compact Lie groups.
Page 1