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 › peer-review

3 Citations (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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10.4153/CJM-2009-043-3

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title = "Maximal operators associated with vector polynomials of lacunary coefficients",

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.",

author = "Sunggeum Hong and Joonil Kim and Yang, {Chan Woo}",

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AU - Hong, Sunggeum

AU - Kim, Joonil

AU - Yang, Chan Woo

PY - 2009/8

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N2 - 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.

AB - 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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U2 - 10.4153/CJM-2009-043-3

DO - 10.4153/CJM-2009-043-3

M3 - Article

AN - SCOPUS:68849108117

VL - 61

SP - 807

EP - 827

JO - Canadian Journal of Mathematics

JF - Canadian Journal of Mathematics

SN - 0008-414X

IS - 4

ER -

Maximal operators associated with vector polynomials of lacunary coefficients

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