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- Title
ON THE UNIFORM CONVERGENCE AND INTEGRABILITY OF SPECIAL TRIGONOMETRIC INTEGRALS.
- Authors
KÓRUS, PÉTER; SZAL, BOGDAN
- Abstract
Abstract. Necessary and sufficient conditions for the uniform convergence of trigonometric Fourier integrals are well-established when admissible monotone or general monotone functions are considered. In this paper, we generalize these main results by giving such conditions for the uniform convergence of sine and cosine integrals ∫∞0 f1 (x) sin (uxp) dx and ∫∞0 f2(x) cos (uxp) dx in case of admissible general monotone functions f1 and f2. Moreover, we give necessary and sufficient conditions for the Lq -integrability with the power weights of these integrals when non-negative functions f1 and f2 belong to the class GMpθ.
- Subjects
FOURIER integrals; INTEGRALS
- Publication
Mathematical Inequalities & Applications, 2024, Vol 27, Issue 1, p1
- ISSN
1331-4343
- Publication type
Article
- DOI
10.7153/mia-2024-27-01