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Integrability of Double Power Series with Nonnegative Coefficients

✍ Scribed by S.M Mazhar; F Móricz

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
168 KB
Volume
219
Category
Article
ISSN
0022-247X

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✦ Synopsis

We consider the double power series

with coefficients a G 0 for all j and k. Among others, we prove exact estimates of jk certain weighted L p -norms of f on the unit square, in terms of the coefficients a . Our results extend those of Askey and Boas, Hardy and Littlewood, Khan, jk Leindler, Mateljevic and Pavlovic from single to double power series. The further ´éxtension to multiple power series is also indicated.

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