On the theorem of Ivasev-Musatov. II
As in Part I [Annales de l’Inst. Fourier, 27-3 (1997), 97-113], our object is to construct a measure whose support has Lebesgue measure zero, but whose Fourier transform drops away extremely fast.
On the Translation Invariance of Wavelet Subspaces.
On the uniform convergence of double sine series
Let a single sine series (*) be given with nonnegative coefficients . If is a “mean value bounded variation sequence” (briefly, MVBVS), then a necessary and sufficient condition for the uniform convergence of series (*) is that as k → ∞. The class MVBVS includes all sequences monotonically decreasing to zero. These results are due to S. P. Zhou, P. Zhou and D. S. Yu. In this paper we extend them from single to double sine series (**) , even with complex coefficients . We also give a uniform...
On the uniform convergence of weighted trigonometric series
In the present paper we consider a new class of sequences called GM(β,r), which is the generalization of a class defined by Tikhonov in [15]. We obtain sufficient and necessary conditions for uniform convergence of weighted trigonometric series with (β,r)-general monotone coefficients.
On the uniform convexity of the Besicovitch-Orlicz space of almost periodic functions with Orlicz norm
In [5], we characterized the uniform convexity with respect to the Luxemburg norm of the Besicovitch-Orlicz space of almost periodic functions. Here we give an analogous result when this space is endowed with the Orlicz norm.
On the uniqueness of periodic decomposition
Let be arbitrary nonzero real numbers. An -decomposition of a function f:ℝ → ℝ is a sum where is an -periodic function. Such a decomposition is not unique because there are several solutions of the equation with -periodic. We will give solutions of this equation with a certain simple structure (trivial solutions) and study whether there exist other solutions or not. If not, we say that the -decomposition is essentially unique. We characterize those periods for which essential uniqueness...
On the utility of the Telyakovskiĭ's class .
On the variance of the number of real roots of a random trigonometric polynomial.
On the weak space and singular measures
We study the class of singular measures whose Fourier partial sums converge to 0 in the metric of the weak space; symmetric sets of constant ratio occur in an unexpected way.
On the weighted estimate of the Bergman projection
We present a proof of the weighted estimate of the Bergman projection that does not use extrapolation results. This estimate is extended to product domains using an adapted definition of Békollé-Bonami weights in this setting. An application to bounded Toeplitz products is also given.
On unconditional convergence of Haar series
On uniform convergence of Fourier series.
On uniform convergence of Hermite series
On vector-valued Fourier multiplier theorems
On vector-valued Hardy martingales and a generalized Jensen's inequality.
On weighted integrability of functions defined by trigonometric series.
On weighted norm inequalities for the maximal function
On weighted transplantation and multipliers for Laguerre expansions.
On Λ-bounded variation
One-sided approximation by trigonometric polynomials in -norm, 0