Related papers: Pointwise multipliers of Orlicz function spaces an…

We give an almost complete description of the coarse and uniform embeddability between Orlicz sequence spaces. We show that the embeddability between two Orlicz sequence spaces is in most cases determined only by the values of their upper…

In this paper, convergence results in a multivariate setting have been proved for a family of neural network operators of the max-product type. In particular, the coefficients expressed by Kantorovich type means allow to treat the theory in…

We introduce connections between the Cuntz relations and the Hardy space H_2 of the open unit disk . We then use them to solve a new kind of multipoint interpolation problem in H_2, where for instance, only a linear combination of the…

In this paper, the Orlicz addition of measures is proposed and an interpretation of the $f$-divergence is provided based on a linear Orlicz addition of two measures. Fundamental inequalities, such as, a dual functional…

This paper aims to extend to Orlicz-Sobolev spaces some results of integral representation for the simultaneous homogenization and dimensional reduction of integral energies defined on fields taking values on a differentiable manifold.…

In this article, we present some results about Fourier multipliers on Hardy spaces in the product case. We mainly give descriptions of multipliers from the space $H^1(\mathbb{T}\times\mathbb{T})$ into the space $\ell^2$ and from the space…

We derive two multivariate generating functions for three-dimensional Young diagrams (also called plane partitions). The variables correspond to a colouring of the boxes according to a finite Abelian subgroup G of SO(3). We use the vertex…

We define as a distribution the product of a function (or distribution) h in some Hardy space Hp with a function b in the dual space of Hp. Moreover, we prove that the product bxh may be written as the sum of an integrable function with a…

For the Hardy-Littlewood maximal and Calder\'on-Zygmund operators, the weighted boundedness on the Lebesgue spaces are well known. We extend these to the Orlicz-Morrey spaces. Moreover, we prove the weighted boundedness on the weak…

N-functions and their growth and regularity properties are crucial in order to introduce and study Orlicz classes and Orlicz spaces. We consider N-functions which are given in terms of so-called associated weight functions. These functions…

For $\alpha\in(0, n)$ and a growth function $\varphi:[0,\infty)\rightarrow [0,\infty)$, it is proved that the commutator $[b,I_\alpha]$ generated by fractional integral operator $I_\alpha$ and Orlicz $\mathrm{BMO}$ function $b$ is bounded…

In this article, we study certain transcendental function spaces arising in potential theory within the framework of Orlicz spaces. Specifically, we generalize Bessel and Lizorkin-Triebel spaces to the nonstandard setting of Orlicz spaces.…

We introduce noncommutative weak Orlicz spaces associated with a weight and study their properties. We also define noncommutative weak Orlicz-Hardy spaces and characterize their dual spaces.

This thesis explores two important areas in the mathematical analysis of nonlinear partial differential equations: Generalized gradient flows and vector valued Orlicz spaces. The first part deals with the existence of strong solutions for…

We derive in this preprint the exact up to multiplicative constant non-asymptotical estimates for the norms of some non-linear in general case operators, for example, the so-called maximal functional operators, in two probabilistic…

We develop a theory of multiplicative functions (with values inside or on the unit circle) in arithmetic progressions analogous to the well-known theory of primes in arithmetic progressions.

We study a.e. convergence on $L^p$, and Lorentz spaces $L^{p,q}$, $p>\tfrac{2d}{d-1}$, for variants of Riesz means at the critical index $d(\tfrac 12-\tfrac 1p)-\tfrac12$. We derive more general results for (quasi-)radial Fourier…

Orlicz spaces are generalizations of Lebesgue spaces. The sufficient and necessary conditions for generalized H\"{o}lder's inequality in Lebesgue spaces and in weak Lebesgue spaces are well known. The aim of this paper is to present…

We introduce generalized Campanato spaces $\mathcal{L}_{p,\phi}$ on a probability space $(\Omega,\mathcal{F},P)$, where $p\in[1,\infty)$ and $\phi:(0,1]\to(0,\infty)$. If $p=1$ and $\phi\equiv1$, then $\mathcal{L}_{p,\phi}=\mathrm{BMO}$. We…

Given an Orlicz space $ L^2 \subseteq X \subseteq L^1$ on $[0,1]$, with submultiplicative Young function ${\mathrm{Y}_X}$, we fully characterize the closed null sets $\Xi$ of the real line with the property that H\"ormander-Mihlin or…