Growth of maximal functions
نویسندگان
چکیده
Abstract. We consider the integrability of φ(f∗) for various maximal functions f∗ and various increasing functions φ. We show that for some of the standard maximal functions arising in harmonic analysis and ergodic theory, there is never integrability of φ(f∗) for all Lebesgue integrable functions f except in cases where the growth of φ is slow enough so that the integrability follows from the standard weak maximal inequalities.
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تاریخ انتشار 2012