Open Access

Weighted integrals of holomorphic functions in the unit polydisc

Journal of Inequalities and Applications20052005:463631

DOI: 10.1155/JIA.2005.583

Received: 28 September 2003

Published: 31 October 2005

Abstract

Let https://static-content.springer.com/image/art%3A10.1155%2FJIA.2005.583/MediaObjects/13660_2003_Article_1534_IEq1_HTML.gif be a measurable function defined on the unit polydisc https://static-content.springer.com/image/art%3A10.1155%2FJIA.2005.583/MediaObjects/13660_2003_Article_1534_IEq2_HTML.gif in https://static-content.springer.com/image/art%3A10.1155%2FJIA.2005.583/MediaObjects/13660_2003_Article_1534_IEq3_HTML.gif and let https://static-content.springer.com/image/art%3A10.1155%2FJIA.2005.583/MediaObjects/13660_2003_Article_1534_IEq4_HTML.gif , https://static-content.springer.com/image/art%3A10.1155%2FJIA.2005.583/MediaObjects/13660_2003_Article_1534_IEq5_HTML.gif , be admissible weights on the unit disk https://static-content.springer.com/image/art%3A10.1155%2FJIA.2005.583/MediaObjects/13660_2003_Article_1534_IEq6_HTML.gif , with distortion functions https://static-content.springer.com/image/art%3A10.1155%2FJIA.2005.583/MediaObjects/13660_2003_Article_1534_IEq7_HTML.gif , https://static-content.springer.com/image/art%3A10.1155%2FJIA.2005.583/MediaObjects/13660_2003_Article_1534_IEq8_HTML.gif , where https://static-content.springer.com/image/art%3A10.1155%2FJIA.2005.583/MediaObjects/13660_2003_Article_1534_IEq9_HTML.gif , and https://static-content.springer.com/image/art%3A10.1155%2FJIA.2005.583/MediaObjects/13660_2003_Article_1534_IEq10_HTML.gif . We prove the following result: if https://static-content.springer.com/image/art%3A10.1155%2FJIA.2005.583/MediaObjects/13660_2003_Article_1534_IEq11_HTML.gif and for all https://static-content.springer.com/image/art%3A10.1155%2FJIA.2005.583/MediaObjects/13660_2003_Article_1534_IEq12_HTML.gif , https://static-content.springer.com/image/art%3A10.1155%2FJIA.2005.583/MediaObjects/13660_2003_Article_1534_IEq13_HTML.gif , then https://static-content.springer.com/image/art%3A10.1155%2FJIA.2005.583/MediaObjects/13660_2003_Article_1534_IEq14_HTML.gif and there is a positive constant https://static-content.springer.com/image/art%3A10.1155%2FJIA.2005.583/MediaObjects/13660_2003_Article_1534_IEq15_HTML.gif such that https://static-content.springer.com/image/art%3A10.1155%2FJIA.2005.583/MediaObjects/13660_2003_Article_1534_IEq16_HTML.gif .

Authors’ Affiliations

(1)
Mathematical Institute of Serbian Academy of Science

Copyright

© Stević 2005