We prove Lp estimates of a class of parametric Marcinkiewicz integral operators when their kernels satisfy only the L1(Sn − 1) integrability condition. The obtained Lp estimates resolve a problem left open in previous work. Our argument is based on duality technique and direct estimation of operators. As a consequence of our result, we deduce the Lp boundedness of a class of fractional Marcinkiewicz integral operators.
- Marcinkiewicz integrals
- Marcinkiewicz interpolation theorem
- parametric Marcinkiewicz functions
- rough kernels
ASJC Scopus subject areas
- Mathematics (miscellaneous)