Sharp norm estimates for a class of integral operators

ABSTRACT

Norm comparison inequalities for two integral operators with radial kernels are established. Sharp norm estimates for operators with monotone and convex/concave kernels are obtained. Integral analogues of Bennett's estimates for summability matrices are given. The exact operator norms with power weights are also obtained for a class of integral operators with radial quasimonotone kernels.

KEYWORDS:

• Weighted inequalities
• norm estimates
• integral operators

2000 MATHEMATICS SUBJECT CLASSIFICATIONS:

• Primary 26D10
• Secondary 47G10

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Funding

This work was supported by the Ministry of Science and Technology, Taipei, ROC, under grants [MOST 105-2115-M-214-003] and [MOST 103-2632-M-214-001-MY3].