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We show that the Riesz fractional integration operator I α(·) of variable order on a bounded open set in Ω ⊂ ℝn in the limiting Sobolev case is bounded from L p(·)(Ω) into BMO(Ω), if p(x) satisfies the standard logcondition and α(x) is Hölder continuous of an arbitrarily small order.
MSC: Primary 46E30; Secondary 26A33, 43A85
Keywords: fractional integral; Riesz potential; variable exponent Lebesgue space; variable order; BMO
[1] D. Cruz-Uribe, L. Diening and P. Hästö, The maximal operator on weighted variable Lebesgue spaces. Fract. Calc. Appl. Anal. 14, No 3 (2011), 361–374; DOI: 10.2478/s13540-011-0023-7; at http://link.springer.com/journal/13540/14/3 CrossrefGoogle Scholar
[2] L. Diening, Maximal function on generalized Lebesgue spaces L p(·). Math. Inequal. Appl. 7, No 2 (2004), 245–253. Google Scholar
[3] L. Diening, P. Harjulehto, Hästö, and M. Růžička, Lebesgue and Sobolev Spaces with Variable Exponents. Springer-Verlag, Lecture Notes in Mathematics, Vol. 2017, Berlin, 2011 http://dx.doi.org/10.1007/978-3-642-18363-8CrossrefGoogle Scholar
[4] V. Kokilashvili, On a progress in the theory of integral operators in weighted Banach function spaces. In: ”Function Spaces, Differential Operators and Nonlinear Analysis”, Proc. of the Conference held in Milovy, Bohemian-Moravian Uplands, May 28–June 2, 2004. Math. Inst. Acad. Sci. Czech Republic, Praha. Google Scholar
[5] O. Kovácĭk and J. Rákosnĭk, On spaces L p(x) and W k,p(x). Czechoslovak Math. J. 41, No 11116 (1991), 592–618 Google Scholar
[6] B. Muckenhoupt and R.L. Wheeden, Weighted norm inequalities for fractional integrals. Trans. Amer. Math. Soc. 192 (1974), 261–274. http://dx.doi.org/10.1090/S0002-9947-1974-0340523-6CrossrefGoogle Scholar
[7] S. Samko, Convolution and potential type operators in L p(x). Integr. Transf. and Special Funct. 7, No 3–4 (1998), 261–284. http://dx.doi.org/10.1080/10652469808819204CrossrefGoogle Scholar
[8] S. Samko, Convolution type operators in L p(x). Integr. Transf. and Special Funct. 7, No 1–2 (1998), 123–144. http://dx.doi.org/10.1080/10652469808819191CrossrefGoogle Scholar
[9] S. Samko, On local summability of Riesz potentials in the case Re a ¿0. Analysis Mathematica 25 (1999), 205–210. http://dx.doi.org/10.1007/BF02908437CrossrefGoogle Scholar
[10] S. Samko, Hypersingular Integrals and their Applications. Taylor & Francis, Series ”Analytical Methods and Special Functions”, Vol. 5, London-New-York, 2002, 358 + xvii pages. Google Scholar
[11] S. Samko, On a progress in the theory of Lebesgue spaces with variable exponent: maximal and singular operators. Integr. Transf. and Spec. Funct. 16, No 5–6 (2005), 461–482. http://dx.doi.org/10.1080/10652460412331320322CrossrefGoogle Scholar
[12] S. Samko, Weighted estimates of truncated potential kernels in the variable exponent setting. Compl. Variabl. Ellipt. Equat. 56, No 7–9 (2011), 813–828. http://dx.doi.org/10.1080/17476931003728396CrossrefGoogle Scholar
[13] E. M. Stein and A. Zygmund, Boundedness of translation invariant operators on Hölder spaces and L p-spaces. Ann. of Math. (2) 85 (1967), 337–349. http://dx.doi.org/10.2307/1970445CrossrefGoogle Scholar
Published Online: 2013-03-19
Published in Print: 2013-06-01
Citation Information: Fractional Calculus and Applied Analysis, Volume 16, Issue 2, Pages 370–377, ISSN (Online) 1314-2224, ISSN (Print) 1311-0454, DOI: https://doi.org/10.2478/s13540-013-0023-x.
© 2013 Diogenes Co., Sofia. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0
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