The Martingale Hardy Type Inequalities for Dyadic Derivative and Integral |
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| Authors: | Jian Ying Nie Xing Guo Li Guo Wei Lou |
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| Institution: | (1) Institute of Near Sensing Technique with Millimeter Wave & Optical Wave, Nanjing University of Science & Technology, Nanjing 210094, P. R. China;(2) School of Mathematics & Computer Science, Fuzhou University, Fuzhou, 350002, P. R. China;(3) Institute of Near Sensing Technique with Millimeter Wave & Optical Wave, Nanjing University of Science & Technology, Nanjing 210094, P. R. China;(4) Present address: Institute of Near Sensing Technique with Millimeter Wave & Optical Wave, Nanjing University of Science & Technology, 200 Xiao Ling Wei, Nanjing 210094, P. R. China |
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| Abstract: | Since the Leibniz–Newton formula for derivatives cannot be used in local fields, it is important to investigate the new concept
of derivatives in Walsh–analysis, or harmonic analysis on local fields. On the basis of idea of derivatives introduced by
Butzer, Schipp and Wade, Weisz has proved that the maximal operators of the one–dimensional dyadic derivative and integral
are bounded from the dyadic Hardy space H
p,q
to L
p,q
, of weak type (L
1
,L
1
), and the corresponding maximal operators of the two–dimensional case are of weak type
. In this paper, we show that these maximal operators are bounded both on the dyadic Hardy spaces H
p
and the hybrid Hardy spaces
.
Research supported by the Preliminary Research Foundation of National Defense (No. 00J5.2.2BQ) and the Foundation of Fuzhou
University (No. 0030824649) |
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| Keywords: | martingale Hardy space dyadic derivative dyadic integral Walsh-Fejer kernels p-atom quasi-local operator |
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