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We prove Lp estimates of a class of parametric Marcinkiewicz integral operators when their kernels satisfy only the \(L^1(\mathbb{S}^{n-1})\) integrability condition. The obtained Lp estimates resolve a problem left open… Click to show full abstract
We prove Lp estimates of a class of parametric Marcinkiewicz integral operators when their kernels satisfy only the \(L^1(\mathbb{S}^{n-1})\) 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.
Keywords:
parametric marcinkiewicz;
rough parametric;
certain rough;
estimates certain;
marcinkiewicz functions;
marcinkiewicz
Journal Title: Frontiers of Mathematics in China
Year Published: 2019
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Journal Title: Frontiers of Mathematics in China
Year Published: 2019
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!