Browsing by Author "Salah Ben Mahmoud"

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    Some Properties Of Function Spaces Of Besov-Type And Applications
    (Université de M'sila, 2022) Salah Ben Mahmoud
    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