On the Littlewood-Paley $g$-function and the Lusin $s$-function

On the littlewood-paley and lusin functions in higher dimensions.

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...

Littlewood-Paley g-Functions and Multipliers for the Laguerre Hypergroup

The concentration function problem for $G$-spaces

‎In this note‎, ‎we consider the concentration function problem for a continuous action of a locally compact group $G$ on a locally compact Hausdorff space $X$‎. ‎We prove a necessary and sufficient condition for the concentration functions of a‎ ‎spread-out irreducible probability measure $mu$ on $G$ to converge to zero.

Bellman function, Littlewood-Paley estimates and asymptotics for the Ahlfors-Beurling operator in L(C)

Estimation of L norms of Fourier multipliers is known to be hard. It is usually connected to some interesting types of PDE, see several such PDE for several Fourier multipliers on the line in a recent paper of Kalton and Verbitsky [13]. Sometimes, but much more rarely, one can establish sharp L estimates for Fourier multipliers in several variables. Riesz transforms are examples of success. The...