We give a characterization of the weights u(·) and v(·) for which the fractional maximal operator Ms is bounded from the weighted Lebesgue spaces Lp(lr, vdx) into Lq(lr, udx) whenever 0 ≤ s < n, 1 < p, r < ∞, and 1 ≤ q < ∞.

We obtain a necessary and sufficient condition for the lacunary polynomials to be dense in weighted Lp spaces of functions on the real line. This generalizes the solution to the classical Bernstein problem given by Izumi, Kawata and Hall. © 2005 Elsevier Inc. All rights reserved.

In this paper, we characterize the bonudedness and compactness of weighted composition operators from weighted Bergman spaces to weighted Bloch spaces. Also, we investigate weighted composition operators on weighted Bergman spaces and extend the obtained results in the unit ball of $mathbb{C}^n$.

Let L = −div(A(x)∇) be a second order elliptic operator with real, symmetric, bounded measurable coefficients on Rn or on a bounded Lipschitz domain subject to Dirichlet boundary condition. For any fixed p > 2, a necessary and sufficient condition is obtained for the boundedness of the Riesz transform ∇(L)−1/2 on the Lp space. As an application, for 1 < p < 3+ ε, we establish the Lp boundedness...

This article is devoted to studying individual ergodic theorems for subsequential weighted averages on the noncommutative Lp-spaces associated a semifinite von Neumann algebra M. In particular, we establish convergence of these along sequences with density one and certain types block positive lower density, extend known results uniform in sense Brunel Keane.

This paper continues the study of the mixed problem for the Laplacian. We consider a bounded Lipschitz domain Ω ⊂ Rn, n ≥ 2, with boundary that is decomposed as ∂Ω = D ∪ N , D and N disjoint. We let Λ denote the boundary of D (relative to ∂Ω) and impose conditions on the dimension and shape of Λ and the sets N and D. Under these geometric criteria, we show that there exists p0 > 1 depending on ...

where the supremum is taken over all cubes Q ⊂ R containing the point x. In [5], L. Diening proved the following remarkable result: if p− > 1, p+ < ∞ and M is bounded on Lp(·), then M is bounded on L (·), where p′(x) = p(x) p(x)−1 . Despite its apparent simplicity, the proof in [5] is rather long and involved. In this paper we extend Diening’s theorem to weighted variable Lebesgue spaces L p(·)...

In 14] and 11] we have studied compact embeddings of weighted function spaces on R n , p 2 (R n), s1 > s2, 1 < p1 p2 < 1, s1 ? n=p1 > s2 ? n=p2, and w(x) of the type w(x) = (1 + jxj) (log(2 + jxj)) , 0, 2 R. We have determined the asymptotic behaviour of the corresponding entropy numbers e k (idH). Now we are interested in the limiting case s1 ?n=p1 = s2 ?n=p2. of the so modiied embedding idH;a...