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Convergence and integrability of rational and double rational trigonometric series with coefficients of bounded variation of higher order

  • Hardeepbhai J. Khachar ORCID logo EMAIL logo and Rajendra G. Vyas ORCID logo
Published/Copyright: June 27, 2023
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Abstract

We prove that a rational trigonometric series with its coefficients c ( n ) = o ( 1 ) satisfying the condition n | Δ m c ( n ) | < , m , converges pointwise to some f ( x ) for every x ( 0 , 2 π ) and also converges in L p [ 0 , 2 π ) -metric to f for 0 < p < 1 m . This result is further extended to a double rational trigonometric series.

MSC 2020: 42C05

Award Identifier / Grant number: 09/0114(11228)/2021-EMR-I

Funding statement: The work of the first author is supported by the Council of Scientific & Industrial Research (CSIR), India, through JRF (File no. 09/0114(11228)/2021-EMR-I).

References

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Received: 2022-08-07
Revised: 2023-01-22
Accepted: 2023-02-14
Published Online: 2023-06-27
Published in Print: 2023-10-01

© 2023 Walter de Gruyter GmbH, Berlin/Boston

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