In this article we develop the theory of H-Orlicz space generated by generalised Young function. Modular convergence for case vector-valued functions and norm in $$\mathcal {H}^\theta (X, \overline{\mu })$$ where X is any Banach are discussed. Relationships modular spaces

STEIN and TAIFJLESON gave a characterization for f E Lp(IRn) to be in the spaces L i p ( a , Lp) and Zyg(a, L p ) in terms of their Poisson integrals. In this paper we extend their results to Lipschitz-Orlicz spaces Lip (cp, L M ) and Zygmund-Orlicz spaces Zyg (cp, L M ) and to the general function cp E P instead of the power function cp(t) = t a . Such results describe the behavior of the Lapl...

The Sobolev spaces have played an essential role in the research of partial differential equations ever since the mid thirties. In order to handle boundary value problems, and, in particular, traces, the more general scales of space have been introduced, namely Slobodeckii spaces and Besov spaces. It proved that Besov spaces are a suitable replacement for Sobolev spaces in many situations and t...

In this work we investigate the approximation problems in the Smirnov-Orlicz spaces in terms of the fractional modulus of smoothness. We prove the direct and inverse theorems in these spaces and obtain a constructive descriptions of the Lipschitz classes of functions defined by the fractional order modulus of smoothness, in particular. 1. Preliminaries and introduction A function M (u) : R → R ...

Recommended by Ricardo Estrada Let X be a Banach space and let L Φ (I,X) denote the space of Orlicz X-valued integrable functions on the unit interval I equipped with the Luxemburg norm. In this paper, we present a distance formula dist Φ This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in a...

The paper investigates some classes of real number sequences over 2-normed spaces defined by means of Orlicz functions, a bounded sequence of strictly positive real numbers, a multiplier and a normal paranormed sequence space. Relevant properties of such classes have been investigated. Moreover, relationships among different such classes of sequences have also been studied under various paramet...

*Correspondence: [email protected] 2Department of Mathematics, Aligarh Muslim University, Aligarh, 202002, India Full list of author information is available at the end of the article Abstract In the present paper we introduce double sequence spacem2(M,A,φ ,p,‖·, . . . , ·‖) defined by a sequence of Orlicz functions over n-normed space. We examine some of its topological properties and estab...

We prove optimal embeddings for nonlinear approximation spaces Aq , in terms of weighted Lorentz sequence spaces, with the weights depending on the democracy functions of the basis. As applications we recover known embeddings for N -term wavelet approximation in L, Orlicz, and Lorentz norms. We also study the “greedy classes” G α q introduced by Gribonval and Nielsen, obtaining new counterexamp...

In this article, we first prove Orlicz norm inequalities for the composition of the homotopy operator and the projection operator acting on solutions of the nonhomogeneous A-harmonic equation. Then we develop these estimates to L (μ)averaging domains. Finally, we give some specific examples of Young functions and apply them to the norm inequality for the composite operator. 2000 Mathematics Sub...