By means of Muckenhoupt type conditions, we characterize the weights ω on C such that Bergman projection Fα2,ℓ=H(C)∩L2(C,e−α2|z|2ℓ), α>0, ℓ>1, is bounded Lp(C,e−αp2|z|2ℓω(z)), for 1<p<∞. We also obtain explicit representation integral formulas functions in weighted spaces Ap(ω)=H(C)∩Lp(ω). Finally, check validity so called Sarason conjecture about boundedness products certain Toeplitz operators...

Korovkin-type theorem which is one of the fundamental methods in approximation theory to describe uniform convergence of any sequence of positive linear operators is discussed on weighted Lp spaces, 1 ≤ p < ∞ for univariate and multivariate functions, respectively. Furthermore, we obtain these types of approximation theorems by means of A-summability which is a stronger convergence method than ...

Our study of abstract quasi-linear parabolic problems in time-weighted Lp-spaces, begun in [17], is extended in this paper to include singular lower order terms, while keeping low initial regularity. The results are applied to reactiondiffusion problems, including Maxwell-Stefan diffusion, and to geometric evolution equations like the surface-diffusion flow or the Willmore flow. The method pres...

Abstract. Let u(x, t) be the solution to the free time-dependent Schrödinger equation at the point (x, t) in space-time Rn+1 with initial data f . We characterize the size of u in terms Lp(Lq)-estimates with power weights. Our bounds are given by norms of f in homogeneous Sobolev spaces Ḣs (Rn). Our methods include use of spherical harmonics, uniformity properties of Bessel functions and interp...

This article is concerned with frame constructions on domains and manifolds. The starting point is a unitary group representation which is square integrable modulo a suitable subgroup and therefore gives rise to a generalized continuous wavelet transform. Then generalized coorbit spaces can be defined by collecting all functions for which this wavelet transform is contained in a weighted Lp-spa...

In this paper we consider unbounded weighted conditional type (WCT) operators on Lp-space. We provide some conditions under which WCT Lp-spaces are densely defined. Specifically, obtain a dense subset of their domain. Moreover, get that operator is continuous if and only it every where A description polar decomposition, spectrum, spectral radius, normality hyponormality in context provided. Fin...

Weighted composition operators appear in the study of dynamical systems and also in characterizing isometries of some classes of Banach spaces. One of the most important generalizations of weighted composition operators, are generalized weighted composition operators which in special cases of their inducing functions give different types of well-known operators like: weighted composition operat...

We investigate the regularity of linear stochastic parabolic equations with zero Dirichlet boundary condition on bounded Lipschitz domains O ⊂ R with both theoretical and numerical purpose. We use N.V. Krylov’s framework of stochastic parabolic weighted Sobolev spaces H p,θ(O, T ). The summability parameters p and q in space and time may differ. Existence and uniqueness of solutions in these sp...

In this paper, we introduce the notion of probabilistic valued measures as a generalization of non-negative measures and construct the corresponding Lp spaces, for distributions p > "0. It is alsoshown that if the distribution p satises p "1 then, as in the classical case, these spaces are completeprobabilistic normed spaces.