Sharp weighted bounds for fractional integrals via the two-weight theory. (English) Zbl 1402.42018

Kokilashvili, Vakhtang; Meskhi, Alexander; Zaighum, Muhammad Asad

Banach J. Math. Anal. 12, No. 3, 673-692 (2018).

Summary: We derive sharp weighted norm estimates for positive kernel operators on spaces of homogeneous type. Similar problems are studied for one-sided fractional integrals. Bounds of weighted norms are of mixed type. The problems are studied using the two-weight theory of positive kernel operators. As special cases, we derive sharp weighted estimates in terms of Muckenhoupt characteristics.

MSC:

42B20	Singular and oscillatory integrals (Calderón-Zygmund, etc.)
42B25	Maximal functions, Littlewood-Paley theory

Keywords:

positive kernels; potentials; fractional maximal functions; spaces of homogeneous type

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