On Convexity of Composition and Multiplication Operators on Weighted Hardy Spaces

Abstract

A bounded linear operator T on a Hilbert space H, satisfying T 2 h 2 h 2 ≥ 2 Th 2 for every h ∈ H, is called a convex operator. In this paper, we give necessary and sufficient conditions under which a convex composition operator on a large class of weighted Hardy spaces is an isometry. Also, we discuss convexity of multiplication operators.

Multiplication Operator with BMO Symbols and Berezin Transform

“…Multiplication operators are one of the most widely studied classes of concrete operators. The study of their behavior on the Hardy and Bergman spaces has generated an extensive list of results in the operator theory and in the theory of function spaces [1][2][3][4][5][6]. One of the useful approaches is the use of the Berezin transform [7][8][9][10][11].…”

Refinements of Hardy-Type Inequalities

“…Later, in 1981, Chan in [2] derived several exponential generalizations of the Imoru's inequalities (5). In 1985, Imoru in [7] presented further extensions of (5).…”