We prove L^P estimates of a class of parametric Marcinkiewicz integral operators when their kernels satisfy only the L^1(S^n-1)integrability condition.The obtained L^P estimates resolve a problem left open in previous...We prove L^P estimates of a class of parametric Marcinkiewicz integral operators when their kernels satisfy only the L^1(S^n-1)integrability condition.The obtained L^P 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 L^P boundedness of a class of fractional Marcinkiewicz integral operators.展开更多
In this note, we obtain sharp Lp estimates of parametric Marcinkiewicz integral operators. Our result resolves a long standing open problem. Also, we present a class of parametric Marcinkiewicz integral operators that...In this note, we obtain sharp Lp estimates of parametric Marcinkiewicz integral operators. Our result resolves a long standing open problem. Also, we present a class of parametric Marcinkiewicz integral operators that are bounded provided that their kernels belong to the sole space L^1(S^n-1).展开更多
文摘We prove L^P estimates of a class of parametric Marcinkiewicz integral operators when their kernels satisfy only the L^1(S^n-1)integrability condition.The obtained L^P 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 L^P boundedness of a class of fractional Marcinkiewicz integral operators.
文摘In this note, we obtain sharp Lp estimates of parametric Marcinkiewicz integral operators. Our result resolves a long standing open problem. Also, we present a class of parametric Marcinkiewicz integral operators that are bounded provided that their kernels belong to the sole space L^1(S^n-1).
