Sharp Hardy’s inequalities in Hilbert spaces
Copyright policy )Sharp Hardy’s inequalities in Hilbert spaces
We study the behavior of the smallest possible constants d(a,b) and d_{n} in Hardy’s inequalities \int_{a}^{b}\biggl(\frac{1}{x}\int_{a}^{x}f(t)dt\biggr)^{2}\:dx\leq d(a,b){}\int_{a}^{b} [f(x)]^{2}\: dx and \sum_{k=1}^{n}\Big(\frac{1}{k}\sum_{j=1}^{k}a_{j}\Big)^{2}\leq d_{n}{}\sum_{k=1}^{n}a_{k}^{2}. The exact constant d(a,b) and the precise rate of convergence of d_{n} are established and the extremal function and the “almost extremal” sequence are found.
- University of Central Florida United States
- Sofia University Bulgaria
- Sao Paulo State University Brazil
Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.), extremal function, Mathematics - Classical Analysis and ODEs, exact constant, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Inequalities for sums, series and integrals, Inequalities involving derivatives and differential and integral operators, Hardy's inequality, Primary 26D10, 26D15, Secondary 33D45, almost extremal sequence
Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.), extremal function, Mathematics - Classical Analysis and ODEs, exact constant, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Inequalities for sums, series and integrals, Inequalities involving derivatives and differential and integral operators, Hardy's inequality, Primary 26D10, 26D15, Secondary 33D45, almost extremal sequence
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