We study a.e. convergence on L, and Lorentz spaces L, p > 2d d−1 , for variants of Riesz means at the critical index d( 1 2 − 1 p )− 1 2 . We derive more general results for (quasi-)radial Fourier multipliers and associated maximal functions, acting on L spaces with power weights, and their interpolation spaces. We also include a characterization of boundedness of such multiplier transformation...

The aim of this paper is to define the lower and upper limits on the family of IF-events with product. We compare two concepts of almost everywhere convergence and we show that they are equivalent, too.

Let Jμ denote the Bessel function of order μ. The functions xJα+β+2n+1(x 1/2), n = 0, 1, 2, . . . , form an orthogonal system in L2((0,∞), xα+βdx) when α+ β > −1. In this paper we analyze the range of p, α and β for which the Fourier series with respect to this system converges in the Lp((0,∞), xαdx)-norm. Also, we describe the space in which the span of the system is dense and we show some of ...

For weighted L space on the unit sphere of R, in which the weight functions are invariant under finite reflection groups, a maximal function is introduced and used to prove the almost everywhere convergence of orthogonal expansions in h-harmonics. The result applies to various methods of summability, including the de la Vallée Poussin means and the Cesàro means. Similar results are also establi...

This survey paper is based on a talk given at the 44th Summer Symposium in Real Analysis Paris. line of research was initiated by question Haight and Weizsäker concerning almost everywhere convergence properties series form $\sum_{n=1}^{{\infty}}f(nx)$. A more general, additive version this problem following: Suppose $\Lambda$ discrete infinite set nonnegative real numbers. We say that $ {\Lamb...

Abstract The concept of Vilenkin–Lebesgue points was introduced in [12], where the almost everywhere convergence Fejer means Vilenkin–Fourier series proved. In this paper, we present a different (and simpler) approach to prove similar result, which can be used that corresponding result holds also more general context, namely for regular Norlund and T -means.

Abstract We prove and discuss some new weak type $(1,1 ) $ ( 1 , ) inequalities of maximal operators Vilenkin–Nörlund means generated by monotone coefficients. Moreover, we use these results to a.e. convergence such means. As applications, both well-known are...