Maximal operators associated with vector polynomials of lacunary coefficients

Sunggeum Hong; Joonil Kim; Chan Woo Yang

doi:10.4153/CJM-2009-043-3

Maximal operators associated with vector polynomials of lacunary coefficients

Sunggeum Hong, Joonil Kim, Chan Woo Yang

Department of Mathematics

Research output: Contribution to journal › Article

1 Citation (Scopus)

Abstract

We prove the L^p(,R^d) (1 < p< ∞) boundedness of the maximal operators associated with a family of vector polynomials given by the form {(2^K₁ P₁(t)., 2^K_d'p_d(f)) : t σ R}. Furthermore, by using the lifting argument, we extend this result to a general class of vector polynomials whose coefficients are of the form constant times 2^K.

Original language	English
Pages (from-to)	807-827
Number of pages	21
Journal	Canadian Journal of Mathematics
Volume	61
Issue number	4
DOIs	https://doi.org/10.4153/CJM-2009-043-3
Publication status	Published - 2009 Aug

ASJC Scopus subject areas

Mathematics(all)

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Hong, S., Kim, J., & Yang, C. W. (2009). Maximal operators associated with vector polynomials of lacunary coefficients. Canadian Journal of Mathematics, 61(4), 807-827. https://doi.org/10.4153/CJM-2009-043-3

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abstract = "We prove the Lp(,Rd) (1 < p< ∞) boundedness of the maximal operators associated with a family of vector polynomials given by the form {(2K1 P1(t)., 2Kd'pd(f)) : t σ R}. Furthermore, by using the lifting argument, we extend this result to a general class of vector polynomials whose coefficients are of the form constant times 2K.",

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