scholarly journals Reflection symmetric Erdélyi-Kober type operators — A quasi-particle interpretation

2014 ◽  
Vol 17 (4) ◽  
Author(s):  
Richard Herrmann
Keyword(s):  
Fractional Integral ◽  
Integral Operators ◽  
Particle Systems ◽  
Quantum Model ◽  
Classical Approach ◽  
Fractional Quantum ◽  
Quasi Particle ◽  
Fractional Integral Operators ◽  
Creation And Annihilation Operators ◽  
Particle Interpretation

AbstractThe reflection symmetric Erdélyi-Kober type fractional integral operators are used to construct fractional quasi-particle generators. The eigenfunctions and eigenvalues of these operators are given analytically. A set of fractional creation- and annihilation-operators is defined and the properties of the corresponding free Hamiltonian are investigated. Analogously to the classical approach for interacting multi-particle systems, the results are interpreted as a fractional quantum model for a description of residual interactions of pairing type.

scholarly journals On integral inequalities related to the weighted and the extended Chebyshev functionals involving different fractional operators

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Barış Çelik ◽  
Mustafa Ç. Gürbüz ◽  
M. Emin Özdemir ◽  
Erhan Set
Keyword(s):  
Fractional Integral ◽  
Integral Operators ◽  
Integral Inequalities ◽  
Fractional Operators ◽  
Fractional Integral Operators

AbstractThe role of fractional integral operators can be found as one of the best ways to generalize classical inequalities. In this paper, we use different fractional integral operators to produce some inequalities for the weighted and the extended Chebyshev functionals. The results are more general than the available classical results in the literature.

scholarly journals Two-weight norm inequalities for fractional integral operators with $A_{\lambda,\infty}$ weights

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Junren Pan ◽  
Wenchang Sun
Keyword(s):  
Fractional Integral ◽  
Integral Operators ◽  
Type Estimate ◽  
Norm Inequalities ◽  
Fractional Integral Operators ◽  
New Class ◽  
Formula Type

Abstract In this paper, we introduce a new class of weights, the $A_{\lambda, \infty}$Aλ,∞ weights, which contains the classical $A_{\infty}$A∞ weights. We prove a mixed $A_{p,q}$Ap,q–$A_{\lambda,\infty}$Aλ,∞ type estimate for fractional integral operators.

On Chebychev type inequalities for fractional integral operators

2017 ◽  
Author(s):  
Fuat Usta ◽  
Hüseyin Budak ◽  
Mehmet Zeki Sarıkaya
Keyword(s):  
Fractional Integral ◽  
Integral Operators ◽  
Fractional Integral Operators

Weighted Norm Inequalities for Fractional Integral Operators With Rough Kernel

1998 ◽  
Vol 50 (1) ◽  
pp. 29-39 ◽  
Author(s):  
Yong Ding ◽  
Shanzhen Lu
Keyword(s):  
Integral Operator ◽  
Fractional Integral ◽  
Integral Operators ◽  
Rough Kernel ◽  
Degree Zero ◽  
Weighted Norm ◽  
Weighted Norm Inequalities ◽  
Norm Inequalities ◽  
Fractional Integral Operators ◽  
Image Position

AbstractGiven function Ω on ℝn , we define the fractional maximal operator and the fractional integral operator by and respectively, where 0 < α < n. In this paper we study the weighted norm inequalities of MΩα and TΩα for appropriate α, s and A(p, q) weights in the case that Ω∈ Ls(Sn-1)(s> 1), homogeneous of degree zero.

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