Hardy-type inequalities for the generalized Mehler transform

We establish Hardy-type inequalities for the generalized Mehler transform on the real Hardy space H^p, 0 < p < 1

Hardy\u27s inequalities for Hermite and Laguerre expansions

金沢大学大学院自然科学研究科機能開発システム金沢大学工学部The well-known inequality of Hardy for Fourier coefficients of functions f(t) ∼ ∑∞n=-∞ bneint in the real Hardy space is ∑∞n=-∞ |bn|/(|n| + 1) < ∞. We shall establish analogues of this inequality for the Hermite function expansions and also for the Laguerre function expansions

Laguerre and Disk Polynomial Expansions with Nonnegative Coefficients

We establish Wiener type theorems and Paley type theorems for Laguerre polynomial expansions and disk polynomial expansions with nonnegative coefficients. © 2013 Springer Science+Business Media New York

Hardy\u27s inequalities for Hermite and Laguerre expansions revisited

金沢大学理工研究域機械工学系We show that Hardy\u27s inequalities for Laguerre expansions hold on the space L1(0, ∞) when the Laguerre parameters α are positive, and we prove that although the inequality holds on the real Hardy space H 1(0, ∞) if α = 0, it does not hold on L1(0, ∞). Further, Hardy\u27s inequality for Hermite expansion is established on L1(0,∞). © 2011 The Mathematical Society of Japan.発行後3年より全文公開 / 出版者照会