Weighted Estimates for Rough Maximal Functions with Applications to Angular Integrability

In this note we establish certain weighted estimates for a class of maximal functions with rough kernels along “polynomial curves” on Rn. As applications, we obtain the bounds of the above operators on the mixed radial-angular spaces, on the vector-valued mixed radial-angular spaces, and on the vect...

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Bibliographic Details
Published in:Journal of function spaces 2019, Vol.2019 (2019), p.1-10
Main Authors: Liu, Feng, Xu, Fangfang
Format: Article
Language:English
Subjects:
Fourier transforms
Function space
Functions (mathematics)
Integrals
Mathematical analysis
Mathematics
Operators (mathematics)
Partial differential equations
Polynomials
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Summary:In this note we establish certain weighted estimates for a class of maximal functions with rough kernels along “polynomial curves” on Rn. As applications, we obtain the bounds of the above operators on the mixed radial-angular spaces, on the vector-valued mixed radial-angular spaces, and on the vector-valued function spaces. Particularly, the above bounds are independent of the coefficients of the polynomials in the definition of the operators.
ISSN:2314-8896
2314-8888
DOI:10.1155/2019/4976351