Some Properties Of Function Spaces Of Besov-Type And Applications
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Date
2022
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Publisher
Université de M'sila
Abstract
In this thesis we introduce new equivalent characterizations and certain commutator
estimations on Besov spaces, Besov-type spaces and Triebel-Lizorkin spaces of variable
smoothness and integrability.
We prove the continuous characterization of the space B ( )
p( ),q( ) and characterization via
Peetre-type maximal functions of local means of variable Besov spaces B ( )
p( ),q( ) based on
the continuous version of Calderón reproducing formula and and of variable Besov-type
spaces B ( ),
p( ),q( ). We prove certain estimates on Triebel-Lizorkin spaces of variable smoothness
and integrability F ( )
p( ),q( ) for the commutator [V r, j ](f ), these estimates are obtained
under no vanishing assumptions on the divergence of the vector field
Description
Keywords
Besov space, Triebel-Lizorkin space, variable exponent,Calderón reproducing formula