In this paper we introduce atomic Hardy spaces on the product domain and prove that rough singular integral operators with Hardy space function kernels are bounded on . This is an extension of some well known results.
The efficient evaluation of a discrete convolution is usually carried out as a repated evaluation of a discrete convolution of a special type with the help of the fast Fourier transform. The paper is concerned with the analysis of the roundoff errors in the fast computation of this convolution. To obtain a comparison, the roundoff errors in the usual (direct) computation of this convolution are also considered. A stochastic model of the propagation of roundoff errors. is employed. The theoretical...
Following Beurling's ideas concerning sampling and interpolation in the Paley-Wiener space Lτ∞, we find necessary and sufficient density conditions for sets of sampling and interpolation in the Paley-Wiener spaces Lτp for 0 < p ≤ 1.
We study the interplay between unconditional decompositions and the R-boundedness of collections of operators. In particular, we get several multiplier results of Marcinkiewicz type for -spaces of functions with values in a Banach space X. Furthermore, we show connections between the above-mentioned properties and geometric properties of the Banach space X.
Let be a second order divergence form elliptic operator with complex bounded measurable coefficients. The operators arising in connection with , such as the heat semigroup and Riesz transform, are not, in general, of Calderón-Zygmund type and exhibit behavior different from their counterparts built upon the Laplacian. The current paper aims at a thorough description of the properties of such operators in , Sobolev, and some new Hardy spaces naturally associated to . First, we show that the...
A measure is called -improving if it acts by convolution as a bounded operator from to L² for some q < 2. Interesting examples include Riesz product measures, Cantor measures and certain measures on curves. We show that equicontractive, self-similar measures are -improving if and only if they satisfy a suitable linear independence property. Certain self-affine measures are also seen to be -improving.
In this article, the structure of semiclassical measures for solutions to the linear Schrödinger equation on the torus is analysed. We show that the disintegration of such a measure on every invariant lagrangian torus is absolutely continuous with respect to the Lebesgue measure. We obtain an expression of the Radon-Nikodym derivative in terms of the sequence of initial data and show that it satisfies an explicit propagation law. As a consequence, we also prove an observability inequality, saying...