scholarly journals On a Refined Operator Version of Young's Inequality and Its Reverse

2019 ◽  
Vol 35 ◽  
pp. 441-448
Author(s):  
Alemeh Sheikhhosseini ◽  
Maryam Khosravi
Keyword(s):  
Young’S Inequality ◽  
Schmidt Norm ◽  
Operator Version ◽  
Young's Inequality

In this note, some refinements of Young's inequality and its reverse for positive numbers are proved, and using these inequalities, some operator versions and Hilbert-Schmidt norm versions for matrices of these inequalities are obtained.

scholarly journals Hölder regularity for degenerate parabolic equations with variable exponents

2022 ◽  
Vol 40 ◽  
pp. 1-19
Author(s):  
Hamid EL Bahja
Keyword(s):  
Weak Solutions ◽  
Parabolic Equations ◽  
Degenerate Parabolic Equations ◽  
Hölder Regularity ◽  
Variable Exponents ◽  
Young’S Inequality ◽  
Scaling Method ◽  
Degenerate Parabolic ◽  
Young's Inequality ◽  
Holder Regularity

In this paper, we discuss a class of degenerate parabolic equations with variable exponents. By  using the Steklov average and Young's inequality, we establish energy and logarithmicestimates for solutions to these equations. Then based on the intrinsic scaling method, we provethat local weak solutions are locally continuous.

scholarly journals Multiple-Term Refinements of Young Type Inequalities

2016 ◽  
Vol 2016 ◽  
pp. 1-11
Author(s):  
Daeshik Choi
Keyword(s):  
Young’S Inequality ◽  
Young's Inequality

Recently, a multiple-term refinement of Young’s inequality has been proved. In this paper, we show its reverse refinement. Moreover, we will present multiple-term refinements of Young’s inequality involving Kantorovich constants. Finally, we will apply scalar inequalities to operators.

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