Cauchy Problems in Weighted Lebesgue Spaces

Sharp Bounds for General Commutators on Weighted Lebesgue Spaces

We show that if an operator T is bounded on weighted Lebesgue space L(w) and obeys a linear bound with respect to the A2 constant of the weight, then its commutator [b, T ] with a function b in BMO will obey a quadratic bound with respect to the A2 constant of the weight. We also prove that the kth-order commutator T k b = [b, T k−1 b ] will obey a bound that is a power (k + 1) of the A2 consta...

Cauchy Singular Integral Operators in Weighted Spaces of Continuous Functions

We study the Cauchy singular integral operator SwI on (−1, 1), where |w| is a generalized Jacobi weight. This operator is considered in pairs of weighted spaces of continuous functions, where the weights u and v are generalized Jacobi weights with nonnegative exponents such that |w| = u/v. We introduce a certain polynomial approximation space which is well appropriated to serve as domain of def...

Decomposition of Lebesgue Spaces

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...

Weighted Composition Operators from Cauchy Integral Transforms to Logarithmic Weighted-type Spaces

We characterize boundedness and compactness of weighted composition operators from the space of Cauchy integral transforms to logarithmic weighted-type spaces. We also manage to compute norm of weighted composition operators acting between these spaces.