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Your search keyword '"Safi S. Rabie"' showing total 2 results
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2 results on '"Safi S. Rabie"'

1. On Discrete Weighted Lorentz Spaces and Equivalent Relations between Discrete ℓp-Classes

Author

Ravi P. Agarwal, Safi S. Rabie, and Samir H. Saker

Subjects
discrete operators, weighted norm inequalities, self-improving properties, A p –weights, B p –weights, B p * –weights, Thermodynamics, QC310.15-319, Mathematics, QA1-939, Analysis, QA299.6-433
Abstract

In this paper, we study some relations between different weights in the classes Bp,Bp*,Mp and Mp* that characterize the boundedness of the Hardy operator and the adjoint Hardy operator. We also prove that these classes generate the same weighted Lorentz space Λp. These results will be proven by using the properties of classes Bp,Bp*,Mp and Mp*, including the self-improving properties and also the properties of the generalized Hardy operator Hp, the adjoint operator Sq and some fundamental relations between them connecting their composition to their sum.

Published
2023
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2. Self-Improving Properties of Continuous and Discrete Muckenhoupt Weights: A Unified Approach

Author

Maryam M. Abuelwafa, Ravi P. Agarwal, Safi S. Rabie, and Samir H. Saker

Subjects
Algebra and Number Theory, dynamic Hardy’s type inequality, Muckenhoupt weights, self-improving properties, time scales, Logic, Geometry and Topology, Mathematical Physics, Analysis
Abstract

In this paper, we develop a new technique on a time scale T to prove that the self-improving properties of the Muckenhoupt weights hold. The results contain the properties of the weights when T=R and when T=N, and also can be extended to cover different spaces such as T=hN, T=qN, etc. The results will be proved by employing some new refinements of Hardy’s type dynamic inequalities with negative powers proven and designed for this purpose. The results give the exact value of the limit exponent as well as the new constants of the new classes.

Published
2023
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