Abstract
This chapter partly deals with one-sided fractional maximal functions and their various generalizations, among them one-sided maximal functions of Hörmander type. We establish L p↑L v p (1 < p ≤ q < ∞) boundedness criteria which are very easy to verify. The proofs depend heavily on the results on the Riemann-Liouville operator which were derived in the previous chapter. Then follows a study, from the point of view of boundedness and compactness, of potentials on the line, or on a bounded interval, involving power-logarithmic kernels and their multidimensional analogues as well.
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© 2002 Springer Science+Business Media Dordrecht
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Edmunds, D.E., Kokilashvili, V., Meskhi, A. (2002). One-Sided Maximal Functions. In: Bounded and Compact Integral Operators. Mathematics and Its Applications, vol 543. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9922-1_3
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DOI: https://doi.org/10.1007/978-94-015-9922-1_3
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-6018-1
Online ISBN: 978-94-015-9922-1
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