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Spring 2022 On the solution of a class of integral equations using new weighted convolutions
Rita C. Guerra
J. Integral Equations Applications 34(1): 39-58 (Spring 2022). DOI: 10.1216/jie.2022.34.39

Abstract

This paper is devoted to the study of the solvability of a class of integral equations, whose kernel depends on four different functions. To obtain necessary and sufficient conditions for the unique solution of this class of equations, we introduce eight new weighted convolutions associated with the kernel of our equations. Moreover, we obtain two Young-type inequalities associated with each convolution.

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Rita C. Guerra. "On the solution of a class of integral equations using new weighted convolutions." J. Integral Equations Applications 34 (1) 39 - 58, Spring 2022. https://doi.org/10.1216/jie.2022.34.39

Information

Received: 22 February 2021; Revised: 26 May 2021; Accepted: 8 June 2021; Published: Spring 2022
First available in Project Euclid: 11 April 2022

Digital Object Identifier: 10.1216/jie.2022.34.39

Subjects:
Primary: ‎43A32 , 44A20 , 44A35 , 45E10 , 47A05 , 47B48

Keywords: convolution , factorization identity , integral equation , ‎weight function , Young’s inequality

Rights: Copyright © 2022 Rocky Mountain Mathematics Consortium

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Vol.34 • No. 1 • Spring 2022
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