Marcinkiewicz functions on product spaces along surfaces of revolution
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Keywords:
rough integrals, surfaces of revolution, Marcinkiewicz integrals, extrapolation, product domains, L^p boundsAbstract
In this paper, specific Lp bounds for a class of Marcinkiewicz integral operators on product spaces along surfaces of revolution are established whenever the kernel functions are rough in Lq n m ( ) 1 1 . By virtue of the obtained bounds and an extrapolation argument, we prove that the aforementioned operators are bounded on Lp n m ( ) × under rather weaker conditions on the kernel functions. The results in this work represent essential improvements and extensions of several results on Marcinkiewicz operators.
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