On the Existence of Principal Values for the Cauchy Integral on Weighted Lebesgue Spaces for Non-Doubling Measures.
On the existence of steady-state solutions to the Navier-Stokes system for large fluxes
In this paper we deal with the stationary Navier-Stokes problem in a domain with compact Lipschitz boundary and datum in Lebesgue spaces. We prove existence of a solution for arbitrary values of the fluxes through the connected components of , with possible countable exceptional set, provided is the sum of the gradient of a harmonic function and a sufficiently small field, with zero total flux for bounded.
On the existence of wavelets for non-expansive dilation matrices.
Sets which simultaneously tile Rn by applying powers of an invertible matrix and translations by a lattice are studied. Diagonal matrices A for which there exist sets that tile by powers of A and by integer translations are characterized. A sufficient condition and a necessary condition on the dilations and translations for the existence of such sets are also given. These conditions depend in an essential way on the interplay between the eigenvectors of the dilation matrix and the translation lattice...
On the expansion theorem described by spaces.
On the exponential integrability of fractional integrals on spaces of homogeneous type
In this paper we show that the fractional integral of order α on spaces of homogeneous type embeds into a certain Orlicz space. This extends results of Trudinger [T], Hedberg [H], and Adams-Bagby [AB].
On the Fejér kernel functions with respect to the Walsh-Kaczmarz system.
On the Fejér means of bounded Ciesielski systems
We investigate the bounded Ciesielski systems, which can be obtained from the spline systems of order (m,k) in the same way as the Walsh system arises from the Haar system. It is shown that the maximal operator of the Fejér means of the Ciesielski-Fourier series is bounded from the Hardy space to if 1/2 < p < ∞ and m ≥ 0, |k| ≤ m + 1. Moreover, it is of weak type (1,1). As a consequence, the Fejér means of the Ciesielski-Fourier series of a function f converges to f a.e. if f ∈ L₁ as n...
On the finite Fourier transforms of functions with infinite discontinuities.
On the Fourier Coefficients of a Function of Lambda - Bounded Variation
On the Fourier series of functions of bounded Φ-variation
On the Fourier transform, Boehmians, and distributions
We introduce some spaces of generalized functions that are defined as generalized quotients and Boehmians. The spaces provide simple and natural frameworks for extensions of the Fourier transform.
On the Fourier transform of
On the Fourier transform of the symmetric decreasing rearrangements
Inspired by work of Montgomery on Fourier series and Donoho-Strak in signal processing, we investigate two families of rearrangement inequalities for the Fourier transform. More precisely, we show that the behavior of a Fourier transform of a function over a small set is controlled by the behavior of the Fourier transform of its symmetric decreasing rearrangement. In the case, the same is true if we further assume that the function has a support of finite measure.As a byproduct, we also give...
On the Fourier Transformation of Positive, Positive Definite Measure on Commutative Hypergroups, and Dual Convolution Structures.
On the Fourier-Laplace representation of analytic functions in tube domains.
On The Frequency With Which Bounded Functions Have Spectral Gaps
On the function of Marcinkiewicz
On the generalization of the Stein-Weiss theorem for the ergodic Hilbert transform
The Stein-Weiss theorem that the distribution function of the Hilbert transform of the characteristic function of E depends only on the measure of E is generalized to the ergodic Hilbert transform.
On the generalized Fourier transforms associated with Schrödinger operators with long-range perturbations.
On the generalized Hardy's inequality of McGhee, Pigno and Smith and the problem of interpolation between BMO and a Besov space.