MATEMATIČKI VESNIK
МАТЕМАТИЧКИ ВЕСНИК



MATEMATIČKI VESNIK
Some generalizations of Littlewood-Paley inequality in the polydisc
K. L. Avetisyan and R. F. Shamoyan

Abstract

The paper generalizes the well-known inequality of Littlewood-Paley in the polydisc. We establish a family of inequalities which are analogues and extensions of Littlewood-Paley type inequalities proved by Sh.\ Yamashita and D. Luecking in the unit disk. Some other generalizations of the Littlewood-Paley inequality are stated in terms of anisotropic Triebel-Lizorkin spaces. With the help of an extension of Hardy-Stein identity, we also obtain area inequalities and representations for quasi-norms in weighted spaces of holomorphic functions in the polydisc.

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Keywords: Littlewood-Paley inequalities, polydisc, Triebel-Lizorkin spaces, weighted spaces.

MSC: 32A37, 32A36

Pages:  97--110     

Volume  58 ,  Issue  3$-$4 ,  2006