Weighted estimates for the Hankel-, \(\underline{K}\)- and \(Y\)- transformations. (English) Zbl 0808.44008

Emara, Salah A. A.

Arch. Math., Brno 30, No. 1, 29-43 (1994).

The author derives sufficient conditions on the pair of nonnegative functions \(u\) and \(v\) for the validity of the inequality \[ \left[ \int^ \infty_ 0 \bigl | u(x) (Tf)(x) \bigr |^ q dx \right]^{1/q} \leq C \left[ \int^ \infty_ 0 \bigl | v(x) f(x) \bigr |^ pdx \right]^{1/p}, \] for \(0<q<p\) and \(p>1\), where \(T\) is the Hankel-, the \(\underline {K}\)-, or the \(Y\)-transformation.

Reviewer: K.N.Srivastava (Bhopal)

MSC:

44A15	Special integral transforms (Legendre, Hilbert, etc.)
26D10	Inequalities involving derivatives and differential and integral operators

Keywords:

\(\underline {K}\)-transform; \(Y\)-transform; Hankel transform; nonnegative functions; inequality