Related papers: Tractability properties of the discrepancy in Orli…
We consider the problem of integration of d-variate analytic functions defined on the unit cube with directional derivatives of all orders bounded by 1. We prove that the Clenshaw Curtis Smolyak algorithm leads to weak tractability of the…
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…
We study tractability properties of the weighted $L_p$-discrepancy. The concept of {\it weighted} discrepancy was introduced by Sloan and Wo\'{z}\-nia\-kowski in 1998 in order to prove a weighted version of the Koksma-Hlawka inequality for…
The criterion for a point in the unit ball to be a strongly exposed point is given. The necessity and sufficiency conditions for Orlicz-Lorentz spaces to possess strongly exposed property are given. Besides, some useful methods are obtained…
We discuss various forms of the Luxemburg norm in spaces of random vectors with coordinates belonging to the classical Orlicz spaces of exponential type. We prove equivalent relations between some kinds of these forms. We also show when the…
In this paper we discuss the structure of weighted weak Lebesgue spaces and weighted weak Orlicz spaces on $\mathbb{R}^n$. First, we present sufficient and necessary conditions for inclusion relation between weighted weak Lebesgue spaces.…
Embeddings among fractional Orlicz-Sobolev spaces with different smoothness are characterized. The equivalence of their Gagliardo-Slobodeckij norms to norms defined via Littlewood-Paley decompostions, via oscillations, or via Besov type…
Certain inequalities between the values of the modular and the norm in the Orlicz spaces are established. These inequalities are applied then to the theory of solvability of nonlinear integral equations of Hammerstein type.
The aim of this paper is investigating of Orlicz spaces with exponential function and correspondence Orlicz norm: we introduce some new equivalent norms, obtain the tail characterization, study the product of functions in Orlicz spaces etc.…
In this paper we discuss the structure of Orlicz spaces and weak Orlicz spaces on $\mathbb{R}^n$. We obtain some necessary and sufficient conditions for the inclusion property of these spaces. One of the keys is to compute the norm of the…
In this paper the necessary and sufficient conditions were given for Orlicz-Lorentz function space endowed with the Orlicz norm having non-squareness and local uniform non-squareness.
In this paper, several weak Orlicz-Hardy martingale spaces associated with concave functions are introduced, and some weak atomic decomposition theorems for them are established. With the help of weak atomic decompositions, a sufficient…
We comment on recent results in the field of information based complexity, which state (in a number of different settings), that approximation of infinitely differentiable functions is intractable and suffers from the curse of…
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…
The weighted star-discrepancy has been introduced by Sloan and Wo{\'z}niakowski to reflect the fact that in multidimensional integration problems some coordinates of a function may be more important than others. It provides upper bounds for…
In this article we consider the approximation of compact linear operators defined over tensor product Hilbert spaces. Necessary and sufficient conditions on the singular values of the problem under which we can or cannot achieve different…
Let G be a locally compact abelian group, $\omega:G\to (0,\infty)$ be a weight, and ($\Phi$,$\Psi$) be a complementary pair of strictly increasing continuous Young functions. We show that for the weighted Orlicz algebra $L^\Phi_\omega(G)$,…
In this paper, we present some new (in-)tractability results related to the integration problem in subspaces of the Wiener algebra over the $d$-dimensional unit cube. We show that intractability holds for multivariate integration in the…
We prove a general theorem showing that local good-$\lambda$ inequalities imply bounds in certain variable Orlicz spaces. We use this to prove results about variable Orlicz Hardy spaces in the unit disc.
We study unbounded weak supersolutions of elliptic partial differential equations with generalized Orlicz (Musielak--Orlicz) growth. We show that they satisfy the weak Harnack inequality with optimal exponent provided that they belong to a…