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Weighted integral inequalities in Orlicz martingale classes

Under appropriate conditions on Young’s functions Φ 1 and Φ 2 , we give necessary and sufficient conditions in order that weighted integral inequalities hold for Doob’s maximal operator M on martingale Orlicz setting. When Φ 1 = t p and Φ 2 = t q , the inequalities revert to the ones of strong or we... Full description

Journal Title: Science China Mathematics 2011, Vol.54(6), pp.1215-1224
Main Author: Chen, Wei
Other Authors: Liu, PeiDe
Format: Electronic Article Electronic Article
Language: English
Subjects:
ID: ISSN: 1674-7283 ; E-ISSN: 1869-1862 ; DOI: 10.1007/s11425-011-4208-7
Link: http://dx.doi.org/10.1007/s11425-011-4208-7
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recordid: springer_jour10.1007/s11425-011-4208-7
title: Weighted integral inequalities in Orlicz martingale classes
format: Article
creator:
  • Chen, Wei
  • Liu, PeiDe
subjects:
  • martingale Orlicz setting
  • Doob’s maximal operator
  • weighted integral inequality
ispartof: Science China Mathematics, 2011, Vol.54(6), pp.1215-1224
description: Under appropriate conditions on Young’s functions Φ 1 and Φ 2 , we give necessary and sufficient conditions in order that weighted integral inequalities hold for Doob’s maximal operator M on martingale Orlicz setting. When Φ 1 = t p and Φ 2 = t q , the inequalities revert to the ones of strong or weak ( p, q )-type on martingale space.
language: eng
source:
identifier: ISSN: 1674-7283 ; E-ISSN: 1869-1862 ; DOI: 10.1007/s11425-011-4208-7
fulltext: fulltext
issn:
  • 1869-1862
  • 18691862
  • 1674-7283
  • 16747283
url: Link


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descriptionUnder appropriate conditions on Young’s functions Φ 1 and Φ 2 , we give necessary and sufficient conditions in order that weighted integral inequalities hold for Doob’s maximal operator M on martingale Orlicz setting. When Φ 1 = t p and Φ 2 = t q , the inequalities revert to the ones of strong or weak ( p, q )-type on martingale space.
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titleWeighted integral inequalities in Orlicz martingale classes
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abstractUnder appropriate conditions on Young’s functions Φ 1 and Φ 2 , we give necessary and sufficient conditions in order that weighted integral inequalities hold for Doob’s maximal operator M on martingale Orlicz setting. When Φ 1 = t p and Φ 2 = t q , the inequalities revert to the ones of strong or weak ( p, q )-type on martingale space.
copHeidelberg
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doi10.1007/s11425-011-4208-7
pages1215-1224
date2011-05