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.

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

MSC: 32A37, 32A36

Pages:  97$-$110     

Volume  58 ,  Issue  3$-$4 ,  2006