We study the problem of boundedness of fractional integral operators on a variable Herz-type Hardy space \( H{\overset{\cdot }{K}}_{p\left(\cdot \right),q\left(\cdot \right)}^{\alpha \left(\cdot \right)}\left({\mathrm{\mathbb{R}}}^n\right) \) by using the atomic decomposition.
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References
A. Almeida and D. Drihem, “Maximal, potential and singular type operators on Herz spaces with variable exponents,” J. Math. Anal. Appl., 394, No. 2, 781–795 (2012).
Y. Chen, S. Levine, and R. Rao, “Variable exponent, linear growth functionals in image restoration,” SIAM J. Appl. Math., 66, 1383–1406 (2006).
L. Diening, P. Harjulehto, P. Hästö, and M. Růžička, “Lebesgue and Sobolev spaces with variable exponents,” Lecture Notes in Math., 2017, Springer-Verlag, Berlin (2011).
D. Drihem and R. Heraiz, “Herz-type Besov spaces of variable smoothness and integrability,” Kodai Math. J., 40, No. 1, 31–57 (2017).
D. Drihem and F. Seghiri, “Notes on the Herz-type Hardy spaces of variable smoothness and integrability,” Math. Inequal. Appl., 19, 145–165 (2016).
M. Izuki, “Herz and amalgam spaces with variable exponent, the Haar wavelets and greediness of the wavelet system,” East J. Approx., 15, 87–109 (2009).
M. Izuki, “Fractional integrals on Herz–Morrey spaces with variable exponent,” Hiroshima Math. J., 40, 343–355 (2010).
M. Izuki, “Boundedness of sublinear operators on Herz spaces with variable exponent and application to wavelet characterization,” Anal. Math., 36, 33–50 (2010).
M. Izuki and T. Noi, Boundedness of Some Integral Operators and Commutators on Generalized Herz Spaces with Variable Exponents; http://www.sci.osaka-cu.ac.jp/math/OCAMI/preprint/2011/11-15.pdf.
X. Li and D. Yang, “Boundedness of some sublinear operators on Herz spaces,” Illinois J. Math., 40, 484–501 (1996).
S. Lu and D. Yang, “Some characterizations of weighted Herz-type Hardy spaces and their applications,” Acta Math. Sinica (N.S.), 13, 45–58 (1997).
A. Miyachi, “Remarks on Herz-type Hardy spaces,” Acta Math. Sinica (Eng. Ser.), 17, 339–360 (2001).
M. Růžička, “Electrorheological fluids: modeling and mathematical theory,” Lecture Notes in Math., 1748, Springer, Berlin (2000).
S. Samko, “Variable exponent Herz spaces,” Mediterran. J. Math., 10, 2007–2025 (2013).
H. B. Wang and Z. G. Liu, “The Herz-type Hardy spaces with variable exponent and their applications,” Taiwan. J. Math., 16, 1363–1389 (2012).
H. Wang, Z. Liu, and Z. Fe, “Boundedness of fractional integrals on Herz-type Hardy spaces with variable exponent,” Adv. Math. (China), 46, No. 2, 252–260 (2017).
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 72, No. 8, pp. 1034–1046, August, 2020. Ukrainian DOI: 10.37863/umzh.v72i8.6024.
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Heraiz, R. Variable Herz Estimates for Fractional Integral Operators. Ukr Math J 72, 1197–1211 (2021). https://doi.org/10.1007/s11253-020-01857-z
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DOI: https://doi.org/10.1007/s11253-020-01857-z