BOUNDEDNESS FOR RIESZ-TYPE POTENTIAL OPERATORS ON HERZ-MORREY SPACES WITH VARIABLE EXPONENT

摘要

In this paper, the Riesz-type potential operator of variable order beta(x) is shown to be bounded from the Herz-Morrey spaces M(K) over dot(p1, q1(.))(alpha, lambda)(R-n) with variable exponent q(1) (x) into the weighted spaceM(K) over dot(p2, q2(.))(alpha, lambda)(R-n, omega), where omega =(1+vertical bar x vertical bar)(-gamma(x)) with some gamma(x)> 0 and 1/q(1) (x)- 1/q(2) (x) = beta (x) 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 and 1 < q(1)(infinity) <= q(1) (x) <= (q(1))+ < infinity (x is an element of R-n).