On the quantitative Fatou property
The result of this article together with [1] and [4] gives a full quantitative description of a Fatou type property for functions from Hardy classes in the upper half plane.
On the rate of pointwise summability of Fourier series.
On the rate of strong summability by matrix means in the generalized Hölder metric.
On the rate of summability by matrix means in the generalized Hölder metric
We will generalize and improve the results of T. Singh [Publ. Math. Debrecen 40 (1992), 261-271] obtaining the L. Leindler type estimates from [Acta Math. Hungar. 104 (2004), 105-113].
On the refined Heisenberg-Weyl type inequality.
On the regular Sturm-Liouville transform.
On the relation between Gaussian measures and convolution semigroups of local type.
On the representation of functions by trigonometric series
On the strict convexity of the Besicovitch-Orlicz space of almost periodic functions with Orlicz norm.
The problem of strict convexity of the Besicovitch-Orlicz space of almost periodic functions is considered here in connection with the Orlicz norm. We give necessary and sufficient conditions in terms of the function f generating the space.
On the strong Cesàro summability of double orthogonal series
On the strong matrix summability of derived Fourier series.
On the strong maximal function and Zygmund’s class
On the strong summability and approximation of Fourier series
On the summability of Fourier series of functions of Λ-bounded variation
On the theorem of Ivasev-Musatov. I
We give a new version of Ivasev-Musatov’s construction of a measure whose support has Lebesgue measure zero but whose Fourier transform drops away extremely rapidly.
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.