Some aspects of the Bergman and Hardy spaces associated with a class of generalized analytic functions

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Publication date: 30 June 2022

Abstract: For

l a m b d a g e 0

, a

C^{2}

function

f

defined on the unit disk

m a t h b b D

is said to be

l a m b d a

-analytic if

, where

is the (complex) Dunkl operator given by

. The aim of the paper is to study several problems on the associated Bergman spaces

A_{l a m b d a}^{p} (m a t h b b D)

and Hardy spaces

H_{l a m b d a}^{p} (m a t h b b D)

for

p g e 2 l a m b d a / (2 l a m b d a + 1)

, such as boundedness of the Bergman projection, growth of functions, density, completeness, and the dual spaces of

A_{l a m b d a}^{p} (m a t h b b D)

and

H_{l a m b d a}^{p} (m a t h b b D)

, and characterization and interpolation of

A_{l a m b d a}^{p} (m a t h b b D)

.

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