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Boundedness for fractional Hardy-type operator on Herz-Morrey spaces with variable exponent

WU Jianglong
대한수학회 (The Korean Mathematical Society)|2014.03|대한수학회보 (Bulletin of the KMS)|제51권 제2호|pp. 423-435

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키워드

variable exponentHerz-Morrey spaceHardy operatorRiesz potentialweighted estimate
주제분류수학

초록

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).

Abstract

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).

참고문헌 (29)

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