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In this paper, the fractional Hardy-type operator of variable order β(x) is shown to be bounded from the Herz-Morrey spaces M ˙K α, p1 ,q1 (·)(Rn) with variable exponent q1(x) into the weighted space M ˙K , p2 ,q2 (·)(Rn, ω), where ω = (1 + |x|)− (x) with some (x) > 0 and 1/q1 (x) − 1/q2 (x) = β(x)/n when q1 (x) is not necessarily constant at infinity. It is assumed that the exponent q1 (x) satisfies the logarithmic continuity condition both locally and at infinity that 1 < q1(1) q1(x) (q1)+ < 1 (x 2 Rn).
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참고문헌 (28)
참고문헌 신청
[학술지(정기간행
A. Almeida / 2012 / Maximal, potential and singular type operators on Herz spaces with variable exponents / J. Math. Anal. Appl 39 (2) : 781 ~ 795
A. Lerner / 2010 / On some questions related to the maximal operator on variable Lp spaces / Trans. Amer. Math. Soc 362 (8) : 4229 ~ 4242
A. Nekvinda / 2004 / Hardy-Littlewood maximal operator on Lp(x)(Rn) / Math. Inequal. Appl 7 (2) : 255 ~ 265
D. Cruz-Uribe / 2003 / The maximal function on variable Lp spaces / Ann. Acad. Sci. Fenn. Math 28 (1) : 223 ~ 238
A. Almeida / 2012 / Maximal, potential and singular type operators on Herz spaces with variable exponents / J. Math. Anal. Appl 39 (2) : 781 ~ 795
A. Lerner / 2010 / On some questions related to the maximal operator on variable Lp spaces / Trans. Amer. Math. Soc 362 (8) : 4229 ~ 4242
A. Nekvinda / 2004 / Hardy-Littlewood maximal operator on Lp(x)(Rn) / Math. Inequal. Appl 7 (2) : 255 ~ 265
D. Cruz-Uribe / 2003 / The maximal function on variable Lp spaces / Ann. Acad. Sci. Fenn. Math 28 (1) : 223 ~ 238
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