A Schauder basis (xn) of a Banach space X is said to be lower [upper] semi-homogeneous if every normalized block basic sequence of (xn) dominates [is dominated by] the basis. We show that the unit vector basis of a separable Orlicz sequence space `M , with M(1) = 1 is lower [upper] semihomogeneous if and only if M fulfils some kind of super[sub]-multiplicative inequality on the interval[0, 1]. ...

In this note, we provide various two-weight norm estimates of the multi-linear fractional maximal function and weighted between different Orlicz spaces. More precisely, obtain Sawyer-type characterizations for these operators.

In this paper we prove compact embedding of a subspace the fractional Orlicz-Sobolev space $W^{s, G}\left(\mathbb{R}^{N}\right)$ consisting radial functions, our target spaces are Orlicz type. Also, Lions and Lieb type results for $W^{s,G}\left(\mathbb{R}^{N}\right)$ that works together in particular way to get sequence whose weak limit is nontrivial. As an application, study existence solution...

An ideal I is a family of subsets of positive integers N which is closed under taking finite unions and subsets of its elements. In this paper we introduce some ideal convergent double interval valued numbers sequence spaces defined by Orlicz function and study different properties of these spaces. We also establish some inclusion relations among them.

In this paper we study the boundedness properties of certain oscillatory integrals with polynomial phase. We obtain sharp estimates for these oscillatory integrals. By the virtue of these estimates and extrapolation we obtain L boundedness for these oscillatory integrals under rather weak size conditions on the kernel function. Keywords—Fourier transform, oscillatory integrals, Orlicz spaces, B...

There is given a criterion for an arbitrary element from the unit sphere of Musielak-Orlicz function space equipped with the Luxemburg norm to be a point of smoothness. Next, as a corollary, a criterion of smoothness of these spaces is given.

In this paper we define and study two concepts which arise from the notion of de la Vallée-Poussin means, namely: strongly double λ̄convergence defined by Orlicz function and λ̄-statistical convergence and establish a natural characterization for the underline sequence spaces. AMS subject classifications: Primary 40A99; Secondary 40A05

In this article we introduce some I-convergent sequence spaces of fuzzy real numbers defined by Orlicz function and study their different properties such as solidity and symmetricity. The notion of I-convergence generalizes the notion of some particular type of convergence of sequences.

In this paper, the idea of lacunary [Formula: see text]-statistical convergent sequence spaces is discussed which is defined by a Musielak-Orlicz function. We study relations between lacunary [Formula: see text]-statistical convergence with lacunary [Formula: see text]-summable sequences. Moreover, we study the [Formula: see text]-lacunary statistical convergence in probabilistic normed space a...