Hilbert-Type Inequalities Including Some Operators, the Best Possible Constants and Applications: A Survey

DOI10.1007/978-3-319-06554-0_2zbMath1321.26037OpenAlexW90714986MaRDI QIDQ2945420

Tserendorj Batbold, Vandanjav Adiyasuren, Mario Krnić

Publication date: 11 September 2015

Published in: Topics in Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-06554-0_2

zbMATH Keywords

Carleman inequalityHardy inequalityHilbert-type inequalityHilbert inequalitybest possible constantmean operatorKnopp inequality

Mathematics Subject Classification ID

Convergence and divergence of series and sequences (40A05) Gamma, beta and polygamma functions (33B15) Inequalities for sums, series and integrals (26D15) Inequalities involving derivatives and differential and integral operators (26D10)

Related Items (1)

An extended reverse Hardy-Hilbert's inequality in the whole plane

Cites Work

• On a half-discrete inequality with a generalized homogeneous kernel
• A unified treatment of half-discrete Hilbert-type inequalities with a homogeneous kernel
• On a new Hilbert-Hardy-type integral operator and applications
• Multiple Hilbert's type inequalities with a homogeneous kernel
• On a Hardy-Carleman's type inequality
• On half-discrete Hilbert's inequality
• Half-discrete Hilbert-type inequalities with mean operators, the best constants, and applications
• A half-discrete Hilbert-type inequality with a non-homogeneous kernel and two variables
• The best constants in multidimensional Hilbert-type inequalities involving some weighted means operators
• On several new Hilbert-type inequalities involving means operators
• On the multidimensional Hilbert-type inequalities involving the hardy operator
• Some new inequalities similar to Hilbert-type integral inequality with a homogeneous kernel
• A Multidimensional Hilbert-Type Integral Inequality Related to the Riemann Zeta Function
• Hardy-Hilbert's inequality with general homogeneous kernel
• Two new forms of Hilbert integral inequality
• Hilbert-type inequalities involving differential operators, the best constants, and applications
• Multiple Hilbert and Hardy-Hilbert inequalities with non-conjugate parameters
• On the best constant in Hilbert's inequality
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