Related papers: Square functions with general measures

Due to their deep connection with the Riemann zeta function, the asymptotic behavior of mean values of multiple zeta functions has attracted considerable attention. In this paper, we study the mean square values of Hurwitz-type and…

The density of polynomials in a weighted space of infinitely differentiable functions in a multidimensional real space is proved under minimal conditions on weight functions and on differences between weight functions. We apply this result…

We study the sums of squares on cylinders of the form $X \times \mathbb{A}_K$ for a (weakly) factorial curve $C$. We prove the equality of the Pythagoras numbers of the ring of regular functions on the cylinder with that of the field of…

First we prove a Littlewood-Paley diagonalization result for bi-Lipschitz perturbations of the identity map on the real line. This result entails a number of corollaries for the Hilbert transform along lines and monomial curves in the…

The paper is concerned with b-metric and generalized b-metric spaces. One proves the existence of the completion of a generalized b-metric space and some fixed point results. The behavior of Lipschitz functions on b-metric spaces of…

The aim of this work is to define a continuous functional calculus in quaternionic Hilbert spaces, starting from basic issues regarding the notion of spherical spectrum of a normal operator. As properties of the spherical spectrum suggest,…

This note extends a recent result of Mendelson on the supremum of a quadratic process to squared norms of functions taking values in a Banach space. Our method of proof is a reduction by a symmetrization argument and observation about the…

For a Dunford-Schwartz operator in a fully symmetric space of measurable functions of an arbitrary measure space, we prove pointwise convergence of the conventional and weighted ergodic averages.

We characterize the inclusions of weighted classes of entire functions in terms of the defining weights resp. weight systems. First we treat weights defined in terms of a so-called associated weight function where the weight(system) is…

We extend some definitions and give new results about the theory of slice analysis in several quaternionic variables. The sets of slice functions which are respectively slice, slice regular and circular w.r.t. given variables are…

We develop a geometric framework for Hardy's inequality on a bounded domain when the functions do vanish only on a closed portion of the boundary.

We discuss some basic properties of the Sibony functions and pseudometrics.

The purpose of this paper is twofold. One is to enrich from a geometrical point of view the theory of octonionic slice regular functions. We first prove a boundary Schwarz lemma for slice regular self-mappings of the open unit ball of the…

We investigate uniqueness problems for an entire function that shares two small functions of finite order with their difference operators. In particular, we give a generalization of a result in $[2]$.

Let $P$ and $Q$ be polynomials in one variable over an algebraically closed field $k$ of characteristic zero. Let $f$ and $g$ be elements of a function field $\K$ over $k$ such that $P(f)=Q(g).$ We give conditions on $P$ and $Q$ such that…

We show that rough isometries between metric spaces X, Y can be lifted to the spaces of real valued 1-Lipschitz functions over X and Y with supremum metric and apply this to their scaling limits. For the inverse, we show how rough…

We find an integral representation for the generalized hypergeometric function unifying known representations via generalized Stieltjes, Laplace and cosine Fourier transforms. Using positivity conditions for the weight in this…

In this paper, first-order Sobolev-type spaces on abstract metric measure spaces are defined using the notion of (weak) upper gradients, where the summability of a function and its upper gradient is measured by the "norm" of a quasi-Banach…

In this paper we shall consider some famous means such as arithmetic, harmonic, geometric, root square mean, etc. Considering the difference of these means, we can establish. some inequalities among them. Interestingly, the difference of…

We prove that certain mean of the quadratical partial sums of the two-dimensional Walsh-Fourier series are uniformly bounded operators from the Hardy space $H_{p}$ to the space $L_{p}$ for $0<p<1.$