Related papers: Dual spaces to Orlicz - Lorentz spaces

For any operator $T$ whose bilinear form can be dominated by a sparse bilinear form, we prove that $T$ is bounded as a map from $L^1(\widetilde{M}w)$ into weak--$L^1(w)$. Our main innovation is that $\widetilde{M}$ is a maximal function…

We establish the weighted fractional Orlicz-Hardy inequalities for various Orlicz functions. Further, we identify the critical cases for each Orlicz function and prove the weighted fractional Orlicz-Hardy inequalities with logarithmic…

For $\mathbb B^n$ the unit ball of $\mathbb C^n$, we consider Bergman-Orlicz spaces of holomorphic functions in $L^\Phi_\alpha$, which are generalizations of classical Bergman spaces. We characterize the dual space of large Bergman-Orlicz…

Let $\mathscr B$ be a normal quasi-Banach function space with respect to $r_0 \in (0,1]$ and $v_0$, $\omega$ be $v$-moderate, and let $r\in [r_0,\infty ]$. Then we prove that $f$ belongs to the modulation space $M(\omega ,\mathscr B )$, iff…

In this article, the authors first introduce a class of Orlicz-slice spaces which generalize the slice spaces recently studied by P. Auscher et al. Based on these Orlicz-slice spaces, the authors introduce a new kind of Hardy type spaces,…

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…

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 characterize norm one complemented subspaces of Orlicz sequence spaces $\ell_M$ equipped with either Luxemburg or Orlicz norm, provided that the Orlicz function $M$ is sufficiently smooth and sufficiently different from the square…

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…

In this paper we give a unitary approach for the simultaneous study of the convergence of discrete and integral operators described by means of a family of linear continuous functionals acting on functions defined on locally compact…

We discuss variants of construction of measurable subgradients for multivariate convex functions and the problem of characterization of the $\Delta_2$-condition in terms of their directional derivatives. Furthermore we study related basic…

The aim of this paper is to deal with the asymptotics of generalized Orlicz norms when the lower growth rate tends to infinity. $\Gamma$-convergence results and related representation theorems in terms of $L^\infty$ functionals are proven…

In this paper, we identify the duals of Triebel-Lizorkin spaces of generalized smoothness. In some particular cases these function spaces are just weighted Triebel-Lizorkin spaces. To do these, we will be working at the level of sequence…

We provide necessary and sufficient conditions for the coincidence, up to equivalence of the norms, between strong and weak Orlicz spaces. Roughly speaking, this coincidence holds true only for the so-called exponential spaces. We find also…

The aim of this paper is to study two-weight norm inequalities for fractional maximal functions and fractional Bergman operator defined on the upper-half space. Namely, we characterize those pairs of weights for which these maximal…

For displacement convex functionals in the probability space equip\-ped with the Monge-Kantorovich metric we prove the equivalence between the gradient and functional type \L oja\-sie\-wicz inequalities. \chg{We also discuss the more…

Orlicz--Morrey spaces are generalizations of Orlicz spaces and Morrey spaces which were first introduced by Nakai. There are three versions of Orlicz--Morrey spaces, i.e: Nakai's (2004), Sawano--Sugano--Tanaka's (2012), and…

We prove the density of smooth functions in the modular topology in the Musielak-Orlicz-Sobolev spaces essentially extending the results of Gossez \cite{GJP2} obtained in the Orlicz-Sobolev setting. We impose new systematic regularity…

The space of Lam\'e functions of order m is isomorphic to the space of pairs (elliptic curve, Abelian differential) where the differential has a single zero of order 2m at the origin and m double poles with vanishing residues. We describe…

Let $E$ be a rearrangement invariant (r.i.) function space on $[0,1]$, and let $Z_E$ consist of all measurable functions $f$ on $(0,\infty)$ such that $f^*\chi_{[0,1]}\in E$ and $f^*\chi_{[1,\infty)}\in L^2$. We reveal close connections…