A martingale approach to general Franklin systems
We prove unconditionality of general Franklin systems in , where X is a UMD space and where the general Franklin system corresponds to a quasi-dyadic, weakly regular sequence of knots.
A maximal function characterization of weighted Besov-Lipschitz and Triebel-Lizorkin spaces.
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 mean value inequality for positive integral transformations with application to a maximal theorem
A method for the calculus of Bernstein's polynomial.
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.
A moment theory approach to the Riesz theorem on the conjugate function with general measures
A multidimensional distribution sampling theorem
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.
A multiparameter variant of the Salem-Zygmund central limit theorem on lacunary trigonometric series
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.
A multiple Hilbert-type integral inequality with the best constant factor.
A multiplier characterization of analytic UMD spaces
A multiplier in Besov spaces which is not a multiplier in Lebesgue spaces
A multiplier theorem for Fourier series in several variables
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.
A multiplier theorem for Jacobi expansions
A multiplier theorem for the Hankel transform.
Riesz function technique is used to prove a multiplier theorem for the Hankel transform, analogous to the classical Hörmander-Mihlin multiplier theorem (Hörmander (1960)).
A multiplier theorem for ultraspherical series
A Necessary and Sufficient Condition for Dual Weyl-Heisenberg Frames to be Comactly Supported.
A necessary and sufficient condition for the existence of a father wavelet
A Necessary Condition for Calderón-Zygmund Singular Integral Operators.
A necessary condition for HK-integrability of the Fourier sine transform function
The paper is concerned with integrability of the Fourier sine transform function when , where is the space of bounded variation functions vanishing at infinity. It is shown that for the Fourier sine transform function of to be integrable in the Henstock-Kurzweil sense, it is necessary that . We prove that this condition is optimal through the theoretical scope of the Henstock-Kurzweil integration theory.
A new Approach to Temperate Generalized Colombeau Functions
A new approach to the problem of constructing recurrence relations for the Jacobi coefficients