Integral operators with periodic kernels in spaces of integrable functions

2020 ◽  
pp. 3-9
Author(s):  
Oleg Gennadievich Avsyankin ◽  
Keyword(s):  
Integral Operators ◽  
Integrable Functions

scholarly journals On certain new CAUCHY–TYPE fracitioanl integral inequalities and OPIAL–TYPE fractional derivative inequalities

2015 ◽  
Vol 46 (1) ◽  
pp. 67-73 ◽  
Author(s):  
Amit Chouhan
Keyword(s):  
Fractional Derivative ◽  
Fractional Integral ◽  
Integral Operators ◽  
Integral Inequalities ◽  
Future Research ◽  
Cauchy Type ◽  
Fractional Integral Operators ◽  
Integrable Functions ◽  
New Inequalities

The aim of this paper is to establish several new fractional integral and derivative inequalities for non-negative and integrable functions. These inequalities related to the extension of general Cauchy type inequalities and involving Saigo, Riemann-Louville type fractional integral operators together with multiple Erdelyi-Kober operator. Furthermore the Opial-type fractional derivative inequality involving H-function is also established. The generosity of H-function could leads to several new inequalities that are of great interest of future research.

The Hardy Space H1 on Manifolds and Submanifolds

1972 ◽  
Vol 24 (5) ◽  
pp. 915-925 ◽  
Author(s):  
Robert S. Strichartz
Keyword(s):  
Partial Differential Equations ◽  
Hardy Space ◽  
Euclidean Space ◽  
Differential Equations ◽  
Singular Integral ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Riesz Transforms ◽  
Partial Differential ◽  
Integrable Functions

It is well-known that the space L1(Rn) of integrable functions on Euclidean space fails to be preserved by singular integral operators. As a result the rather large Lp theory of partial differential equations also fails for p = 1. Since L1 is such a natural space, many substitute spaces have been considered. One of the most interesting of these is the space we will denote by H1(Rn) of integrable functions whose Riesz transforms are integrable.

scholarly journals Certain Inequalities Involving Generalized Erdélyi-Kober Fractionalq-Integral Operators

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Praveen Agarwal ◽  
Soheil Salahshour ◽  
Sotiris K. Ntouyas ◽  
Jessada Tariboon
Keyword(s):  
Integral Operator ◽  
Fractional Integral ◽  
Integral Operators ◽  
Integral Inequalities ◽  
Integrable Functions ◽  
Special Cases

In recent years, a remarkably large number of inequalities involving the fractionalq-integral operators have been investigated in the literature by many authors. Here, we aim to present some new fractional integral inequalities involving generalized Erdélyi-Kober fractionalq-integral operator due to Gaulué, whose special cases are shown to yield corresponding inequalities associated with Kober type fractionalq-integral operators. The cases of synchronous functions as well as of functions bounded by integrable functions are considered.

scholarly journals New General Variants of Chebyshev Type Inequalities via Generalized Fractional Integral Operators

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 122
Author(s):  
Ahmet Ocak Akdemir ◽  
Saad Ihsan Butt ◽  
Muhammad Nadeem ◽  
Maria Alessandra Ragusa
Keyword(s):  
Fractional Integral ◽  
Integral Operators ◽  
Chebyshev Inequality ◽  
Fractional Integral Operators ◽  
Integrable Functions ◽  
Inequality Theory ◽  
Special Cases ◽  
Generalized Fractional Integral ◽  
Chebyshev's Inequality ◽  
Generalized Fractional Integral Operators

In this study, new and general variants have been obtained on Chebyshev’s inequality, which is quite old in inequality theory but also a useful and effective type of inequality. The main findings obtained by using integrable functions and generalized fractional integral operators have generalized many existing results as well as iterating the Chebyshev inequality in special cases.

scholarly journals A Generalizedq-Grüss Inequality Involving the Riemann-Liouville Fractionalq-Integrals

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Aydin Secer ◽  
S. D. Purohit ◽  
K. A. Selvakumaran ◽  
Mustafa Bayram
Keyword(s):  
Integral Inequality ◽  
Integral Operators ◽  
Grüss Inequality ◽  
Integrable Functions ◽  
Special Cases ◽  
Type Integral

The aim of this paper is to establishq-extension of the Grüss type integral inequality related to the integrable functions whose bounds are four integrable functions, involving Riemann-Liouville fractionalq-integral operators. The results given earlier by Zhu et al. (2012) and Tariboon et al. (2014) follow the special cases of our findings.

Multianisotropic integral operators defined by regular equations

2018 ◽  
Vol 60 (3) ◽  
pp. 610-629
Author(s):  
G. A. Karapetyan ◽  
H. A. Petrosyan
Keyword(s):  
Integral Operators

Multi-parameter Singular Integrals II: General Theory

2017 ◽  
Author(s):  
Brian Street
Keyword(s):  
General Theory ◽  
Singular Integral ◽  
Singular Integrals ◽  
Integral Operators ◽  
Singular Integral Operators ◽  
Main Issue

This chapter turns to a general theory which generalizes and unifies all of the examples in the preceding chapters. A main issue is that the first definition from the trichotomy does not generalize to the multi-parameter situation. To deal with this, strengthened cancellation conditions are introduced. This is done in two different ways, resulting in four total definitions for singular integral operators (the first two use the strengthened cancellation conditions, while the later two are generalizations of the later two parts of the trichotomy). Thus, we obtain four classes of singular integral operators, denoted by A1, A2, A3, and A4. The main theorem of the chapter is A1 = A2 = A3 = A4; i.e., all four of these definitions are equivalent. This leads to many nice properties of these singular integral operators.

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