On boundedness of fractional maximal operator in weighted L^p(.) spaces

Boundedness of the Fractional Maximal Operator in Local Morrey-type Spaces

The problem of the boundedness of the fractional maximal operator Mα, 0 ≤ α < n in local Morrey-type spaces is reduced to the problem of the boundedness of the Hardy operator in weighted Lp-spaces on the cone of non-negative non-increasing functions. This allows obtaining sharp sufficient conditions for the boundedness for all admissible values of the parameters.

On Boundedness of Weighted Hardy Operator in Lp() and Regularity Condition

Maximal regularity for evolution equations in weighted Lp - spaces

LetX be a Banach space and let A be a closed linear operator on X. It is shown that the abstract Cauchy problem u̇(t)+ Au(t) = f (t), t > 0, u(0) = 0, enjoys maximal regularity in weighted Lp-spaces with weights ω(t) = tp(1−μ), where 1/p < μ, if and only if it has the property of maximal Lp-regularity. Moreover, it is also shown that the derivation operator D = d/dt admits anH∞-calculus in weigh...

compactifications and function spaces on weighted semigruops

chapter one is devoted to a moderate discussion on preliminaries, according to our requirements. chapter two which is based on our work in (24) is devoted introducting weighted semigroups (s, w), and studying some famous function spaces on them, especially the relations between go (s, w) and other function speces are invesigated. in fact this chapter is a complement to (32). one of the main fea...

Necessary and Sufficient Conditions for the Boundedness of Dunkl-Type Fractional Maximal Operator in the Dunkl-Type Morrey Spaces

and Applied Analysis 3 For all x, y, z ∈ R, we put Wα ( x, y, z ) : ( 1 − σx,y,z σz,x,y σz,y,x ) Δα ( x, y, z ) , 2.5