Pointwise mutipliers of Orlicz function spaces and factorization

In the paper we find representation of the space of pointwise multipliers between two Orlicz function spaces, which appears to be another Orlicz space and the formula for the Young function generating this space is given. Further, we apply this result to find necessary and sufficient conditions for factorization of Orlicz function spaces.     

Pointwise multipliers for localized morrey-campanato spaces on RD-spaces

In this article, the authors characterize pointwise multipliers for localized Morrey-Campanato spaces, associated with some admissible functions on RD-spaces, which include localized BMO spaces as a special case. The results obtained are applied to Schrödinger operators and some Laguerre operators.     

Pointwise multipliers for Besov spaces of dominating mixed smoothness-Ⅱ

We continue our investigations on pointwise multipliers for Besov spaces of dominating mixed smoothness. This time we study the algebra property of the classes S_(p,q)~rB(R~d) with respect to pointwise multiplication. In addition, if p≤q, we are able to describe the space of all pointwise multipliers for S_(p,q)~rB(R~d).     

Cn中单位球上两个全纯函数空间之间的点乘子

在Cn中单位球上讨论了加权Bergman空间Aαp和Bloch型空间βq之间的点乘子.根据α,p,q的不同情况,得到了Aαp空间到βq空间的所有点乘子,并研究了βq空间到Apα空间的点乘子的性质.     

Pointwise bornological spaces

With each metric space (X,d) we can associate a bornological space (X,Bd) where Bd is the set of all subsets of X with finite diameter. Equivalently, Bd is the set of all subsets of X that are contained in a ball with finite radius. If the metric d can attain the value infinite, then the set of all subsets with finite diameter is no longer a bornology. Moreover, if d is no longer symmetric, then the set of subsets with finite diameter does not coincide with the set of subsets that are contained in a ball with finite radius. In this text we will introduce two structures that capture the concept of boundedness in both symmetric and non-symmetric extended metric spaces.     

Lattice-universal Orlicz spaces on probability spaces

Lattice-universal Orlicz function spacesL ^F _α,β[0, 1] with prefixed Boyd indices are constructed. Namely, given 0<α<β<∞ arbitrary there exists Orlicz function spacesL ^F _α,β[0, 1] with indices α and β such that every Orlicz function spaceL ^G [0, 1] with indices between α and β is lattice-isomorphic to a sublattice ofL ^F _α,β[0, 1]. The existence of classes of universal Orlicz spacesl ^Fα,β(I) with uncountable symmetric basis and prefixed indices α and β is also proved in the uncountable discrete case. Partially supported by BFM2001-1284.     

Polyhedrality in Orlicz spaces

We present a construction of an Orlicz space admitting a C ^∞-smooth bump which depends locally on finitely many coordinates, and which is not isomorphic to a subspace of any C(K), K scattered. In view of the related results this space is possibly not isomorphic to a polyhedral space. Supported by grants: Institutional Research Plan AV0Z10190503, GAČR 201/04/0090, GAČR 201/07/0394, the research project MSM 0021620839, GAČR 201/05/P582.     

Prediction in Orlicz spaces

In this paper, we investigate the prediction (or best approximation) operator from a uniformly convex real Orlicz space to a subset of -lattice measurable functions. In particular, a counterexample to the monotoncity property, which holds in L_p spaces, is given. Also, a sufficient condition for monotonicity to hold is given. Finally, nested -lattices, as occur in isotonic regression, are considered.This author supported by a grant from the Indiana University-Purdue University at Fort Wayne Research and Instructional Development Support Program     

Hardy inequalities in Orlicz spaces

We establish a sharp extension, in the framework of Orlicz spaces, of the (-dimensional) Hardy inequality, involving functions defined on a domain , their gradients and the distance function from the boundary of .

     

Composition operators on Orlicz spaces

In this paper we characterize the composition operators on Orlicz spaces and study some of their properties.Research supported by NBHM DDF No. 40/11/95 (R&D-II)/1429     

Analytic norms in Orlicz spaces

It is shown that an Orlicz sequence space admits an equivalent analytic renorming if and only if it is either isomorphic to or isomorphically polyhedral. As a consequence, we show that there exists a separable Banach space admitting an equivalent -Fréchet norm, but no equivalent analytic norm.

     

Fourier multipliers of Lipschitz spaces

Let G denote an infinite, compact, metrizable, 0-dimensional, Abelian group. The following are characterized: (i) the multipliers from one Lipschitz space Lip(α, p; G) to another Lipschitz space Lip(β, q; G) for 0 < α < β < ∞ and 1 ? p, q ? ∞; and (ii) the multipliers from Lip(α, p; G) to Lip(β, q; G) for 0 < β ? α < ∞ and 1 < q ? 2 ? p < ∞. Two special cases of (i), namely the case q = ∞ and the case p = 1, were obtained by the authors in an earlier publication (1981). A. Zygmund (J. Math. Mech.8 (1959), 889–895) and T. Mizuhara (Tôhoku Math. J.24 (1972), 263–268) have characterized the multipliers of certain Lipschitz spaces defined on the circle group.     

Pointwise lineability in sequence spaces

We continue the research on lineability/spaceability properties in sequence spaces. Our main results show that several theorems in this framework are valid in a stricter sense. To do this job we introduce the notion of pointwise lineability which seems to be of independent interest for further investigations in other environments.