INVERSION OF DOUBLE FOURIER INTEGRAL OF NON-LEBESGUE INTEGRABLE BOUNDED VARIATION FUNCTIONS
Abstract
This work proves pointwise convergence of the truncated
Fourier double integral of non-Lebesgue integrable bounded variation
functions. This leads to the Dirichlet-Jordan theorem proof for non-
Lebesgue integrable functions, which has not been sufficiently studied.
Note that recent contributions regarding this subject consider Lebesgue
integrable functions, [F. Móricz, 2015], [B. Ghodadra-V. Fulop, 2016].
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Published
2025-12-20
Section
Advances in Nonlinear Analysis and Applications
Copyright (c) 2025 Boletim da Sociedade Paranaense de Matemática
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