Nacima Memić

A note on the maximal operators of Vilenkin-Nörlund means with non-increasing coefficients

In [14] we investigated some Vilenkin—Norlund means with non-increasing coefficients. In particular, it was proved that under some special conditions the maximal operators of such summabily methods are bounded from the Hardy space H1/(1+α) to the space weak-L1/(1+α), (0 < α ≦ 1). In this paper we construct a martingale in the space H1/(1+α), which satisfies the conditions considered in [14], and so that the maximal operators of these Vilenkin—Norlund means with non-increasing coefficients are not bounded from the Hardy space H1/(1+α) to the space L1/(1+α). In particular, this shows that the conditions under which the result in [14] is proved are in a sense sharp. Moreover, as further applications, some well-known and new results are pointed out.

Relations between Schramm spaces and generalized Wiener classes

Abstract We give necessary and sufficient conditions for the embeddings Λ BV ( p ) ⊆ Γ BV ( q n ↑ q ) and Φ BV ⊆ BV ( q n ↑ q ) . As a consequence, a number of results in the literature, including a fundamental theorem of Perlman and Waterman, are simultaneously extended.

Strong convergence of two-dimensional Vilenkin-Fourier series

We prove that certain means of the quadratical partial sums of the two-dimensional Vilenkin-Fourier series are uniformly bounded operators from the Hardy space

Sets of Minimality of (1 − 1)-Rational Functions

H_{p}

Ergodic polynomials on subsets of p-adic integers

to the space

A derivative on the field of p-adic numbers

L_{p}

Maximal functions, Hardy spaces and Fourier multiplier theorems on unbounded Vilenkin groups

for

Fourier multiplier theorem for atomic Hardy spaces on unbounded Vilenkin groups

0<p\leq 1.

Ergodic polynomials on 2-adic spheres

We also prove that the sequence in the denominator cannot be improved.

ON PERTURBED MONOMIALS ON 2-ADIC SPHERES AROUND 1

We describe dynamical systems associated to (1 − 1)-rational functions on the field of p-adic numbers.We focus on sets of minimality of such systems.