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Maximal Operators Associated with Vector Polynomials of Lacunary Coefficients

Published online by Cambridge University Press:  20 November 2018

Sunggeum Hong ,
Joonil Kim  and
Chan Woo Yang
Sunggeum Hong
Affiliation:
Department of Mathematics, Chosun University, Gwangju 501-759, Korea, e-mail: [email protected]
Joonil Kim
Affiliation:
Department of Mathematics, Yonsei University, Seoul 120-749, Korea, e-mail: [email protected]
Chan Woo Yang
Affiliation:
Department of Mathematics, Korea University, Seoul 136-701, Korea, e-mail: [email protected]
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Abstract

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We prove the ${{L}^{P}}({{\mathbb{R}}^{d}})(1<p\le \infty )$ boundedness of the maximal operators associated with a family of vector polynomials given by the form $\left\{ ({{2}^{{{k}_{1}}}}{{\mathfrak{p}}_{1}}(t),...,{{2}^{{{k}_{d}}}}{{\mathfrak{p}}_{d}}(t)):t\in \mathbb{R} \right\}$. 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 ${{2}^{k}}$.

Keywords

42B2042B25
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 61 , Issue 4 , 01 August 2009 , pp. 807 - 827
Copyright
Copyright © Canadian Mathematical Society 2012

References

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