We give characterizations of weighted Besov-Lipschitz and Triebel-Lizorkin spaces with weights via a smooth kernel which satisfies “minimal” moment and Tauberian conditions. The results are stated in terms of the mixed norm of a certain maximal function of a distribution in these weighted spaces.
A systematic method for the calculus of Bernstein's polynomial is described. It consists of reducing the problem to a homogeneous linear system of equations that may be constructed by fixed rules. Several problems about its computer implementation are discussed.
Using Bochner-Riesz means we get a multidimensional sampling theorem for band-limited functions with polynomial growth, that is, for functions which are the Fourier transform of compactly supported distributions.
We prove the central limit theorem for the multisequence where , are reals, are partially hyperbolic commuting s × s matrices, and x is a uniformly distributed random variable in . The main tool is the S-unit theorem.
We define a new type of multiplier operators on , where is the N-dimensional torus, and use tangent sequences from probability theory to prove that the operator norms of these multipliers are independent of the dimension N. Our construction is motivated by the conjugate function operator on , to which the theorem applies as a particular example.
Riesz function technique is used to prove a multiplier theorem for the Hankel transform, analogous to the classical Hörmander-Mihlin multiplier theorem (Hörmander (1960)).
Let be a nonnegative Radon measure on which only satisfies for all , , with some fixed constants and In this paper, a new characterization for the space of Tolsa in terms of the John-Strömberg sharp maximal function is established.