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Weighted Integrability of Double Series with Respect to Multiplicative Systems

Abstract

Necessary and sufficient conditions for L p-integrability with power weight of a function f represented by the double series with respect to a multiplicative system with generalized monotone coefficients are obtained. These conditions are given in terms of the coefficients or their second mixed differences. In addition, the integrability of the difference quotient (f(x, y) − f(x, 0) − f(0, y) + f(0, 0))/(xy) is studied.

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Correspondence to S. S. Volosivets.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 18, No. 5, pp. 69–87, 2013.

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Volosivets, S.S., Fadeev, R.N. Weighted Integrability of Double Series with Respect to Multiplicative Systems. J Math Sci 209, 51–65 (2015). https://doi.org/10.1007/s10958-015-2484-4

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Keywords

  • Trigonometric Series
  • Double Sequence
  • Double Series
  • Multiplicative System
  • Power Weight