We prove that any weight v ∈ L1loc(R) v : R → [0,+∞) of the Muckenhoupt class A∞ has the form v = h′ where h : R → R is a bi-Sobolev map. As an application we improve the known results on exact continuation and reciprocal imbeddings for Gehring Gq and Muckenhoupt A p classes, providing exact bounds in all cases.
Sharp interactions among (formula presented.)-weights on the real line / Popoli, A., Sbordone, C., Zecca, G.. - In: RICERCHE DI MATEMATICA. - ISSN 0035-5038. - 64:2(2015), pp. 289-301. [10.1007/s11587-015-0232-1]
Sharp interactions among (formula presented.)-weights on the real line
Popoli A.;
2015
Abstract
We prove that any weight v ∈ L1loc(R) v : R → [0,+∞) of the Muckenhoupt class A∞ has the form v = h′ where h : R → R is a bi-Sobolev map. As an application we improve the known results on exact continuation and reciprocal imbeddings for Gehring Gq and Muckenhoupt A p classes, providing exact bounds in all cases.File allegati a questo prodotto
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