变指标Fofana空间及其预对偶空间

杨凡; 周疆

doi:10.13568/j.cnki.651094.651316.2023.01.19.0001

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变指标Fofana空间及其预对偶空间

更新时间：2026-01-21

- 变指标Fofana空间及其预对偶空间
- Journal of Xinjiang University (Natural Science Edition in Chinese and English) Vol. 40, Issue 5, Pages: 565-581(2023)
- 作者机构：
  
  新疆大学数学与系统科学学院
- 作者简介：
- 基金信息：
- DOI：10.13568/j.cnki.651094.651316.2023.01.19.0001
  CLC： O177
- Published：2023
- 稿件说明：
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[1]杨凡,周疆.变指标Fofana空间及其预对偶空间[J].新疆大学学报(自然科学版)(中英文),2023,40(05):565-581.
[1]杨凡,周疆.变指标Fofana空间及其预对偶空间[J].新疆大学学报(自然科学版)(中英文),2023,40(05):565-581. DOI： 10.13568/j.cnki.651094.651316.2023.01.19.0001.

DOI：10.13568/j.cnki.651094.651316.2023.01.19.0001.

摘要

通过引入变指标Fofana空间(L~(p(·))

Lqα)(Rn)(1

Abstract

By introducing variable Fofana's spaces(Lp(·)

Lq)α(Rn)(1 < p(·) < ∞

1 ≤ q

α ≤ ∞) and their pre-dual spaces

we discussed the properties of those spaces. Meanwhile

via applying hierarchical decomposition of function and real variable techniques

the necessary and sufficient conditions for boundedness of fractional integral operators and their commutators on variable Fofana's spaces are obtained.

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references

ORLICZ W.¨Uber konjugierte exponentenfolgen[J]. Studia Mathematica, 1931, 3:200-212.

KOVAˇCIK O, RAKOSNI J. On spaces Lp(x)and W k,p(x)[J]. Czechoslovak Mathematical Journal, 1991, 41(4):592-618.

FAN X L, ZHAO D. On the spaces Lp(x)(?)and W m,p(x)(?)[J]. Journal of Mathematical Analysis&Applications, 2001, 263(2):424-446.

DIENING L, HARJULEHTO P, H¨AST¨O P, et al. Lebesgue and Sobolev spaces with variable exponents[M]. Berlin:Springerverlag, 2011.

STEIN E M. Singular integrals and differentiability properties of functions[M]. Princeton:Princeton University Press, 1970.

CAPONE C, CRUZ-URIBE D, FIORENZA A. The fractional maximal operator and fractional integrals on variable Lp spaces[J].Revista Matematica Iberoamericana, 2007, 23(3):743-770.

CHANILLO S. A note on commutators[J]. Indiana University Mathematics Journal, 1982, 31(1):7-16.

IZUKI M. Commutators of fractional integrals on Lebesgue and Herz spaces with variable exponent[J]. Rendiconti del Circolo Matematico di Palermo, 2010, 59(3):461-472.

WIENER N. On the representation of functions by trigonometrical integrals[J]. Mathematische Ztschrift, 1926, 24(1):575-616.

HOLLAND F. Harmonic analysis on amalgams of Lp and lq[J]. Journal of the London Mathematical Society, 1975, 3:295-305.

AYDINI, G¨URKANLI A T. Weighted variable exponent amalgam spaces W(Lp(x), Lqw)[J]. Glasnik Matematicki, 2012, 47(1):165-174.

FOFANA I.Etude d’une classe d’espace de fonctions contenant les espaces de Lorentz[J]. Arkiv fo¨r Matematik, 1988, 1(2):29-50.

FEICHTINGER H J, FEUTO J. Pre-dual of Fofana’s spaces[J]. Mathematics, 2019, 7(6):528-538.

ZHANG H K, ZHOU J. Mixed-norm amalgam spaces and their predual[J]. Symmetry, 2022, 14(1):74-100.

CRUZ-URIBE D, FIORENZA A, MARTELL J M, et al. The boundedness of classical operators on variable Lp spaces[J]. Annales Academiae Scientiarum Fennicae Mathematica, 2006, 31(1):239-264.

IZUKI M. Boundedness of sublinear operators on Herz spaces with variable exponent and application to wavelet characterization[J].Analysis Mathematica, 2010, 36(1):33-50.

IZUKI M. Boundedness of commutators on Herz spaces with variable exponent[J]. Rendiconti del Circolo Matematico di Palermo,2010, 59(2):199-213.

JANSON S. Mean oscillation and commutators of singular integral operators[J]. Arkiv for Matematik, 1978, 16:263-270.

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