If {qn} is a lacunary sequence of integers, and if for each n, cn(x) and c-n(x) are trigonometric polynomials of degree n, then {Cn(X)} must tend to zero for almost every x whenever {cn(x)ei?nX + c-n(-x)e-i?'nX} does. We conjecture that a similar result ought to hold even when the sequence {f On} has much slower growth. However, there is a sequence of integers {nj } and trigonometric polynomial...

The Cauchy problem for the Hardy–Hénon parabolic equation is studied in critical and subcritical weighted Lebesgue spaces on Euclidean space R d . In earlier works, well-posedness of singular initial data existence non-radial forward self-similar solutions to were shown Hardy Fujita cases ( ? ? 0 ). are used treat potential | x as an increase or decrease weight, which enables us prove all , wit...

In this paper we study both real and complex interpolation in the recently introduced scales of variable exponent Besov and Triebel–Lizorkin spaces. We also take advantage of some interpolation results to study a trace property and some pseudodifferential operators acting in the variable index Besov scale.

There are several generalizations of the space L1(R) of Lebesgue integrable functions taking values in the real numbers R (and defined on the usual Lebesgue measure space (Ω,Σ, μ) on [0, 1] ) to a space of strongly-measurable “integrable” (suitably formulated) functions taking values in a Banach space X. The most common generalization is the space L1(X) of Bochner-Lebesgue integrable functions....

Let X be an N -parameter additive Lévy process in IR with Lévy exponent (Ψ1, · · · ,ΨN ) and let λd denote Lebesgue measure in IR . We show that E{λd(X(IR+ ))} > 0 ⇐⇒ ∫ IR N ∏ j=1 Re ( 1 1 + Ψj(ξ) ) dξ < ∞. This was previously proved by Khoshnevisan, Xiao and Zhong [1] under a sector condition.

In this paper we establish well posedness of the Neumann problem with boundary data in L2 or the Sobolev space Ẇ 2 −1, in the half space, for linear elliptic differential operators with coefficients that are constant in the vertical direction and in addition are self adjoint. This generalizes the well known well-posedness result of the second order case and is based on a higher order and one si...

This paper shows necessary and sufficient conditions on subsets of variable exponent spaces Lp(?)(?) in order to be weakly compact. Useful criteria are given extending Andô results for Orlicz spaces. As application, we prove that all separable Banach-Saks. Also, L-weakly compact inclusions between studied.