Atomic decomposition of predictable martingale Hardy space with variable exponents

Zhiwei Hao

Czechoslovak Mathematical Journal (2015)

  • Volume: 65, Issue: 4, page 1033-1045
  • ISSN: 0011-4642

Abstract

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This paper is mainly devoted to establishing an atomic decomposition of a predictable martingale Hardy space with variable exponents defined on probability spaces. More precisely, let ( Ω , ℱ , ℙ ) be a probability space and p ( · ) : Ω → ( 0 , ∞ ) be a ℱ -measurable function such that 0 < inf x ∈ Ω p ( x ) ≤ sup x ∈ Ω p ( x ) < ∞ . It is proved that a predictable martingale Hardy space 𝒫 p ( · ) has an atomic decomposition by some key observations and new techniques. As an application, we obtain the boundedness of fractional integrals on the predictable martingale Hardy space with variable exponents when the stochastic basis is regular.

How to cite

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Hao, Zhiwei. "Atomic decomposition of predictable martingale Hardy space with variable exponents." Czechoslovak Mathematical Journal 65.4 (2015): 1033-1045. <http://eudml.org/doc/276255>.

@article{Hao2015,
abstract = {This paper is mainly devoted to establishing an atomic decomposition of a predictable martingale Hardy space with variable exponents defined on probability spaces. More precisely, let $(\Omega , \mathcal \{F\}, \mathbb \{P\})$ be a probability space and $p(\cdot )\colon \Omega \rightarrow (0,\infty )$ be a $\mathcal \{F\}$-measurable function such that $0<\inf \nolimits _\{x\in \Omega \}p(x)\le \sup \nolimits _\{x\in \Omega \}p(x)<\infty $. It is proved that a predictable martingale Hardy space $\mathcal \{P\}_\{p(\cdot )\}$ has an atomic decomposition by some key observations and new techniques. As an application, we obtain the boundedness of fractional integrals on the predictable martingale Hardy space with variable exponents when the stochastic basis is regular.},
author = {Hao, Zhiwei},
journal = {Czechoslovak Mathematical Journal},
keywords = {variable exponent; atomic decomposition; martingale Hardy space; fractional integral},
language = {eng},
number = {4},
pages = {1033-1045},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Atomic decomposition of predictable martingale Hardy space with variable exponents},
url = {http://eudml.org/doc/276255},
volume = {65},
year = {2015},
}

TY - JOUR
AU - Hao, Zhiwei
TI - Atomic decomposition of predictable martingale Hardy space with variable exponents
JO - Czechoslovak Mathematical Journal
PY - 2015
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 65
IS - 4
SP - 1033
EP - 1045
AB - This paper is mainly devoted to establishing an atomic decomposition of a predictable martingale Hardy space with variable exponents defined on probability spaces. More precisely, let $(\Omega , \mathcal {F}, \mathbb {P})$ be a probability space and $p(\cdot )\colon \Omega \rightarrow (0,\infty )$ be a $\mathcal {F}$-measurable function such that $0<\inf \nolimits _{x\in \Omega }p(x)\le \sup \nolimits _{x\in \Omega }p(x)<\infty $. It is proved that a predictable martingale Hardy space $\mathcal {P}_{p(\cdot )}$ has an atomic decomposition by some key observations and new techniques. As an application, we obtain the boundedness of fractional integrals on the predictable martingale Hardy space with variable exponents when the stochastic basis is regular.
LA - eng
KW - variable exponent; atomic decomposition; martingale Hardy space; fractional integral
UR - http://eudml.org/doc/276255
ER -

References

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