Lp Estimates for the Iterated Hardy-Littlewood Maximal Operator on Rn and Kn, K a Local Field

Shijun Zheng; Weiyi Su

doi:10.1007/BF02836766

Lp Estimates for the Iterated Hardy-Littlewood Maximal Operator on Rn and Kn, K a Local Field

Shijun Zheng, Weiyi Su

Mathematical Sciences

Nanjing University, China

Research output: Contribution to journal › Article › peer-review

Abstract

<div class="line" id="line-5"> In light of two measure estimate inequalities from [4] for the iterated Hardy-Littlewood maximal operator M k f, certain equivalence between M k f and the Zygmund class L Log a L are established on <msup><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="double-struck">R</mi></mrow><mi>n</mi></msup></math>' id="MathJax-Element-2-Frame" role="presentation" tabindex="0"> R n , so that we generalize Stein's L Log L theorem. In Section 3, a simple induction enables us to prove such extensions on K n , the n-dimensional linear space over a local field K , without recoursing to Leckband's result.</div>

Original language	American English
Journal	Approximation Theory and its Applications
Volume	14
DOIs	https://doi.org/10.1007/BF02836766
State	Published - Sep 1998

Disciplines

Mathematics

Keywords

Hardy space
Induction hypothesis
Iterate operator
Local field
Weak type

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title = "Lp Estimates for the Iterated Hardy-Littlewood Maximal Operator on Rn and Kn, K a Local Field",

abstract = " In light of two measure estimate inequalities from [4] for the iterated Hardy-Littlewood maximal operator M k f, certain equivalence between M k f and the Zygmund class L Log a L are established on R n , so that we generalize Stein's L Log L theorem. In Section 3, a simple induction enables us to prove such extensions on K n , the n-dimensional linear space over a local field K , without recoursing to Leckband's result.",

keywords = "Hardy space, Induction hypothesis, Iterate operator, Local field, Weak type",

author = "Shijun Zheng and Weiyi Su",

note = "In light of two measure estimate inequalities from [4] for the iterated Hardy-Littlewood maximal operator Mk f, certain equivalence between Mk f and the Zygmund class LLog a L are established on[equation]...",

year = "1998",

month = sep,

doi = "10.1007/BF02836766",

language = "American English",

volume = "14",

journal = "Approximation Theory and its Applications",

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T1 - Lp Estimates for the Iterated Hardy-Littlewood Maximal Operator on Rn and Kn, K a Local Field

AU - Zheng, Shijun

AU - Su, Weiyi

N1 - In light of two measure estimate inequalities from [4] for the iterated Hardy-Littlewood maximal operator Mk f, certain equivalence between Mk f and the Zygmund class LLog a L are established on[equation]...

PY - 1998/9

Y1 - 1998/9

N2 - In light of two measure estimate inequalities from [4] for the iterated Hardy-Littlewood maximal operator M k f, certain equivalence between M k f and the Zygmund class L Log a L are established on R n , so that we generalize Stein's L Log L theorem. In Section 3, a simple induction enables us to prove such extensions on K n , the n-dimensional linear space over a local field K , without recoursing to Leckband's result.

AB - In light of two measure estimate inequalities from [4] for the iterated Hardy-Littlewood maximal operator M k f, certain equivalence between M k f and the Zygmund class L Log a L are established on R n , so that we generalize Stein's L Log L theorem. In Section 3, a simple induction enables us to prove such extensions on K n , the n-dimensional linear space over a local field K , without recoursing to Leckband's result.

KW - Hardy space

KW - Induction hypothesis

KW - Iterate operator

KW - Local field

KW - Weak type

UR - https://link.springer.com/article/10.1007/BF02836766

U2 - 10.1007/BF02836766

DO - 10.1007/BF02836766

M3 - Article

VL - 14

JO - Approximation Theory and its Applications

JF - Approximation Theory and its Applications

ER -

Lp Estimates for the Iterated Hardy-Littlewood Maximal Operator on Rn and Kn, K a Local Field

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