A note on Marcinkiewicz integrals supported by submanifolds

In the present paper, we establish the boundedness and continuity of the parametric Marcinkiewicz integrals with rough kernels associated to polynomial mapping [Formula: see text] as well as the corresponding compound submanifolds, which is defined by [Formula: see text] on the Triebel–Lizorkin spac...

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Detalles Bibliográficos
Autor principal: Liu, Feng
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2018
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6132579/
https://www.ncbi.nlm.nih.gov/pubmed/30839656
http://dx.doi.org/10.1186/s13660-018-1822-8
Descripción
Sumario:In the present paper, we establish the boundedness and continuity of the parametric Marcinkiewicz integrals with rough kernels associated to polynomial mapping [Formula: see text] as well as the corresponding compound submanifolds, which is defined by [Formula: see text] on the Triebel–Lizorkin spaces and Besov spaces when [Formula: see text] and [Formula: see text] for some [Formula: see text] . Our main results represent significant improvements and natural extensions of what was known previously.

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