Applications of Integration in Mathematical Analysis

A special issue of Axioms (ISSN 2075-1680).

Deadline for manuscript submissions: closed (31 May 2023) | Viewed by 1176

Special Issue Editors


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Guest Editor
Sterling College, 125 W Cooper, Sterling, KS 67579, USA
Interests: mathematical analysis; functional analysis; operator theory

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Co-Guest Editor
1. Office for Outer Space Affairs, United Nations, Vienna International Centre, A-1400 Vienna, Austria
2. Centre for Mathematical and Statistical Sciences, Peechi Campus, KFRI, Peechi, Kerala 680653, India
Interests: special functions; fractional calculus; entropic functional; mathematical physics; applied analysis; statistical distributions; geometrical probabilities; multivariate analysis
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Special Issue Information

Dear Colleagues,

The integral has served as a versatile tool in a wide range of mathematical fields, from integral transforms and integral equations to the task of defining linear functionals and norms on function spaces. This Special Issue aims to be a general collection of new and novel results that utilize integration techniques in some capacity. 

We look forward to your contributions to this Special Issue.

Dr. Samuel A. Hokamp
Prof. Dr. Hans J. Haubold
Guest Editors

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Keywords

  • integration
  • integral operators
  • integral transforms
  • integral equations
  • function spaces
  • integrable functions
  • functional analysis
  • measure theory

Published Papers (1 paper)

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Research

16 pages, 329 KiB  
Article
On Certain Estimates for Parabolic Marcinkiewicz Integrals Related to Surfaces of Revolution on Product Spaces and Extrapolation
by Mohammed Ali and Hussain Al-Qassem
Axioms 2023, 12(1), 35; https://doi.org/10.3390/axioms12010035 - 27 Dec 2022
Cited by 2 | Viewed by 931
Abstract
In this paper, appropriate Lp bounds for particular classes of parabolic Marcinkiewicz integrals along surfaces of revolution on product spaces are obtained. These bounds allow us to use Yano’s extrapolation argument to obtain the Lp boundedness of the aforesaid integral operators [...] Read more.
In this paper, appropriate Lp bounds for particular classes of parabolic Marcinkiewicz integrals along surfaces of revolution on product spaces are obtained. These bounds allow us to use Yano’s extrapolation argument to obtain the Lp boundedness of the aforesaid integral operators under weak conditions on the kernels. These conditions on the kernels are the best possible among their respective classes. In this work, several previously known results on Marcinkiewicz integrals are fundamentally improved and extended. Full article
(This article belongs to the Special Issue Applications of Integration in Mathematical Analysis)
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