BOUNDEDNESS FOR FRACTIONAL HARDY-TYPE OPERATOR ON HERZ-MORREY SPACES WITH VARIABLE EXPONENT

作者：Wu Jianglong^*

来源：Bulletin of the Korean Mathematical Society, 2014, 51(2): 423-435.

DOI：10.4134/BKMS.2014.51.2.423

• Herz-Morrey space
• Hardy operator
• Riesz potential
• variable exponent
• weighted estimate

In this paper, the fractional Hardy-type operator of variable order beta(x) is shown to be bounded from the Herz-Morrey spaces Mk(p1,q1(.))(alpha,lambda) (R-n) with variable exponent q1(x) into the weighted space Mk(p2,q2(.))(alpha,lambda) (R-n,w) where w = (1 + vertical bar x vertical bar)(-gamma(x)) with some gamma(x) > 0 and 1/q(1) (x) - 1/q(2) (x) = beta(x)/n when q(1)(x) is not necessarily constant at infinity. It is assumed that the exponent q(1)(x) satisfies the logarithmic continuity condition both locally and at infinity that 1 < q(1)(infinity) <= q(1)(x) <= (q(1))+ < infinity (x is an element of R-n).

• 出版日期2014-3
• 单位牡丹江师范学院