Commutators of the fractional maximal function on variable exponent Lebesgue spaces

On The Sobolev-type Inequality for Lebesgue Spaces with a Variable Exponent

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...

Boundedness of Littlewood-Paley operators and their commutators on Herz-Morrey spaces with variable exponent

The aim of this paper is to establish the vector-valued inequalities for Littlewood-Paley operators, including the Lusin area integrals, the Littlewood-Paley g-functions and g∗μ-functions, and their commutators on the Herz-Morrey spaces with variable exponentMK̇ p,q(·)(R n). By applying the properties of Lp(·)(Rn) spaces and the vector-valued inequalities for Littlewood-Paley operators and their...

On Variable Exponent Amalgam Spaces

We derive some of the basic properties of weighted variable exponent Lebesgue spaces L p(.) w (R) and investigate embeddings of these spaces under some conditions. Also a new family of Wiener amalgam spaces W (L p(.) w , L q υ) is defined, where the local component is a weighted variable exponent Lebesgue space L p(.) w (R) and the global component is a weighted Lebesgue space Lυ (R) . We inves...

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...