Variable Herz estimates for fractional integral operators

R. Heraiz

doi:10.37863/umzh.v72i8.6024

R. Heraiz M’sila Univ., Algeria

DOI: https://doi.org/10.37863/umzh.v72i8.6024

Анотація

УДК 517.5

Змiннi оцiнки Герца для дробових iнтегральних операторiв

За допомогою атомарної декомпозицiї вивчається обмеженiсть дробових iнтегральних операторiв у змiнному просторi Гардi $HK^{\alpha (\cdot )}_{p(\cdot ),q(\cdot )}(\mathbb{R}^n)$ типу Герца.

Посилання

A. Almeida, D. Drihem, Maximal, potential and singular type operators on Herz spaces with variable exponents,J. Math. Anal. and Appl., 394, № 2, 781 – 795, 2012, https://doi.org/10.1016/j.jmaa.2012.04.043 DOI: https://doi.org/10.1016/j.jmaa.2012.04.043

Y. Chen, S. Levine, R. Rao, Variable exponent, linear growth functionals in image restoration, SIAM J. Appl. Math., 66, 1383 – 1406 (2006), https://doi.org/10.1137/050624522 DOI: https://doi.org/10.1137/050624522

L. Diening, P. Harjulehto, P. Hästö, M. Růžička, Lebesgue and Sobolev Spaces withVariable Exponents, Lecture Notes in Mathematics, 2017, Springer-Verlag, Berlin, (2011), https://doi.org/10.1007/978-3-642-18363-8 DOI: https://doi.org/10.1007/978-3-642-18363-8

D. Drihem, Seghiri, F., Notes on the Herz-type Hardy spaces of variable smoothness and integrability, Math. Inequal.and Appl., 19, 145 – 165 (2016), https://doi.org/10.7153/mia-19-11 DOI: https://doi.org/10.7153/mia-19-11

M. Izuki, Herz and amalgam spaces with variable exponent, the Haar wavelets and greediness of the wavelet system, East. J. Approxim., 15, 87 – 109 (2009).

M. Izuki, Fractional integrals on Herz–Morrey spaces with variable exponent, Hiroshima Math. J., 40, 343 – 355 (2010), DOI: https://doi.org/10.32917/hmj/1291818849

M. Izuki, Boundedness of sublinear operators on Herz spaces with variable exponent and application to wavelet characterization, Anal. Math., 36, 33 – 50 (2010), https://doi.org/10.1007/s10476-010-0102-8 DOI: https://doi.org/10.1007/s10476-010-0102-8

M. Izuki, T. Noi, Boundedness of some integral operators and commutators on generalized Herz spaces with variable exponents, https://pdfs.semanticscholar.org/2774/f7507db743a34ba641a47617bcb5e3ea4d31.pdf

X. Li, D. Yang, Boundedness of some sublinear operators on Herz spaces, Illinois J. Math., 40, 484 – 501 (1996). DOI: https://doi.org/10.1215/ijm/1255986021

S. Lu, D. Yang, Some characterizations of weighted Herz-type Hardy spaces and their applications, Acta Math. Sinica(N.S.), 13, 45 – 58 (1997), https://doi.org/10.1007/BF02560523 DOI: https://doi.org/10.1007/BF02560523

A. Miyachi, Remarks on Herz-type Hardy spaces, Acta Math. Sin. (Engl. Ser.), 17, 339 – 360 (2001), https://doi.org/10.1007/s101140100104 DOI: https://doi.org/10.1007/s101140100104

M. Růžička, Electrorheological fluids: modeling and mathematical theory, Lect. Notes Math., 1748, Springer Verlag, Berlin (2000), https://doi.org/10.1007/BFb0104029 DOI: https://doi.org/10.1007/BFb0104029

S. Samko, Variable exponent Herz spaces, Mediterr. J. Math., 10, 2007 – 2025 (2013), https://doi.org/10.1007/s00009-013-0285-x DOI: https://doi.org/10.1007/s00009-013-0285-x

H. B. Wang, Z. G. Liu, The Herz-type Hardy spaces with variable exponent and their applications, Taiwanese J. Math., 16, 1363 – 1389 (2012) , https://doi.org/10.11650/twjm/1500406739 DOI: https://doi.org/10.11650/twjm/1500406739

H. Wang, L. Zongguang, F. Zunwei, Boundedness of fractional integrals on Herz-type Hardy spaces with variable exponent, Adv. Math. (China), 46, № 2, 252 – 260 (2017), https://doi.org/10.11845/sxjz.2015072b