Discrete analogue of generalized Hardy spaces and multiplication operators on homogenous trees

We estimate the essential norm of a compact weighted composition operator acting between different Hardy spaces of the unit ball in . Also we will discuss a compact multiplication operator between Hardy spaces.

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On Convexity of Composition and Multiplication Operators on Weighted Hardy Spaces

Abstract and Applied Analysis ◽

10.1155/2009/931020 ◽

2009 ◽

Vol 2009 ◽

pp. 1-9 ◽

Cited By ~ 2

Author(s):

Karim Hedayatian ◽

Lotfollah Karimi

Keyword(s):

Hilbert Space ◽

Linear Operator ◽

Composition Operator ◽

Hardy Spaces ◽

Bounded Linear Operator ◽

Sufficient Conditions ◽

Multiplication Operators ◽

Weighted Hardy Spaces ◽

Bounded Linear ◽

Necessary And Sufficient

A bounded linear operatorTon a Hilbert spaceℋ, satisfying‖T2h‖2+‖h‖2≥2‖Th‖2for everyh∈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.

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Some Generalized Hardy Spaces

Canadian Journal of Mathematics ◽

10.4153/cjm-1967-055-1 ◽

1967 ◽

Vol 19 ◽

pp. 621-628

Author(s):

L. D. Meeker

Keyword(s):

Banach Space ◽

Hardy Spaces ◽

Analytic Functions ◽

General Setting ◽

Classical Case ◽

Boundary Values ◽

Generalized Hardy Spaces

This paper is concerned with generalizations of the classical Hardy spaces (8, p. 39) and the question of boundary values for functions of these various spaces. The general setting is the “big disk” Δ discussed by Arens and Singer in (1, 2) and by Hoffman in (7). Analytic functions are defined in (1). Classes of such functions corresponding to the Hardy Hp spaces are considered and shown to possess boundary values in (2). Contrary to the classical case, such functions do not form a Banach space; hence they are not the functional analytic analogue of the classical spaces. In (3) quasi-analytic functions are defined while in (4) Hardy spaces of such functions are considered and are shown to have boundary values and to form a Banach space.

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Inner Functions and Isometries

Canadian Mathematical Bulletin ◽

10.4153/cmb-1975-070-3 ◽

1975 ◽

Vol 18 (3) ◽

pp. 383-385 ◽

Cited By ~ 1

Author(s):

Paul S. Muhly

Keyword(s):

Hardy Spaces ◽

Multiplication Operators ◽

Inner Functions ◽

Spectral Behavior

Our objective in this note is to prove a theorem about the spectral behavior of certain multiplication operators. It was motivated by and yields an extension of part of a theorem of Lumer [3] concerning the possibility of imbedding the classical Hardy spaces in abstract ones.

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