New sufficient conditions on the weight functions u(.) and v(.) are given in order that the fractional maximal [resp. integral] operator Ms [resp. Is], 0 ≤ s < n, [resp. 0 < s < n] sends the weighted Lebesgue space Lp(v(x)dx) into Lp(u(x)dx), 1 < p < ∞. As a consequence a characterization for this estimate is obtained whenever the weight functions are radial monotone.
2000 Mathematics Subject Classification: 46B20.Uniform G-convexity of Banach spaces is a recently introduced natural generalization of uniform convexity and of complex uniform convexity. We study conditions under which uniform G-convexity of X passes to the space of X-valued functions Lp (m,X).
Some class of locally solid topologies (called uniformly -continuous) on Köthe-Bochner spaces that are continuous with respect to some natural two-norm convergence are introduced and studied. A characterization of uniformly -continuous topologies in terms of some family of pseudonorms is given. The finest uniformly -continuous topology on the Orlicz-Bochner space is a generalized mixed topology in the sense of P. Turpin (see [11, Chapter I]).
Étude des propriétés des unions et intersections d’espaces relatifs à un ensemble de mesures positives sur un groupe commutatif localement compact lorsque est invariant par translation ou stable par convolution.Dans des cas particuliers, on retrouve les propriétés d’espaces étudiés par A. Beurling et par B. Koremblium.On étudie aussi les espaces formés des fonctions appartenant localement à et qui ont un comportement à l’infini.
The duality between H1 and BMO, the space of functions of bounded mean oscillation (see [JN]), was first proved by C. Fefferman (see [F], [FS]) and then other proofs of it were obtained.In this paper we shall study such space in little more detail and we shall consider the H1-BMO duality for vector-valued functions in the more general setting of spaces of homogeneous type (see [CW]).
Holomorphic and harmonic functions with values in a Banach space are investigated. Following an approach given in a joint article with Nikolski [4] it is shown that for bounded functions with values in a Banach space it suffices that the composition with functionals in a separating subspace of the dual space be holomorphic to deduce holomorphy. Another result is Vitali’s convergence theorem for holomorphic functions. The main novelty in the article is to prove analogous results for harmonic functions...