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Uncertainty Principle Estimates for Vector Fields

✍ Scribed by Carlos Pérez; Richard L. Wheeden

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
275 KB
Volume
181
Category
Article
ISSN
0022-1236

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✦ Synopsis

We derive weighted norm estimates for integral operators of potential type and for their related maximal operators. These operators are generalizations of the classical fractional integrals and fractional maximal functions. The norm estimates are derived in the context of a space of homogeneous type. The conditions required of the weight functions involve generalizations of the Fefferman Phong ``r-bump'' condition. The results improve some earlier ones of the same kind, and they also extend to homogeneous spaces some estimates that were previously known to hold only in the classical Euclidean setting.

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