Multilinear Riesz potential operators on Herz-type spaces and generalized Morrey spaces

作者：Shi Yanlong; Tao Xiangxing^*

来源：Hokkaido Mathematical Journal, 2009, 38(4): 635-662.

DOI：10.14492/hokmj/1258554238

• roultilinear fractional integral
• homogeneous Herz-Morrey space
• Herz-type hardy space
• homogeneous Herz space
• generalized Morrey space

Let in, it be integers with n >= 2, m >= 1, the multilinear Riesz potential operators be defined by
I(alpha)((m))(f)(x)=integral((Rn)m) f(1)(y(1))...f(m)(y(m))/vertical bar(x-y(1),...,x-y(m))vertical bar(mn-alpha) dy,
where y = (y(1),...y(m)) and f = (f(1),...f(m)). In the first part of this paper, the boundedness for the operator I(alpha)((m)) on the homogeneous Herz-Morrey product spaces, M(K) over dot(p1,q1)(n(1-1/q1),lambda 1)(R(n)) x ... x M(K) over dot(pm,qm)(n(1-1/qm),) (lambda m)(R(n)), and on the Herz-type Herdy product spaces, H(K) over dot(q1)(sigma 1,p1)(R(n)) x...x H(K) over dot(qm)(sigma m,pm)(R(n)) for sigma(i) > n(1-1/q(i)), are established respectively. The second goal of the paper is to extend the known L(p)-boundedness of I(alpha)((m)) to generalized Morrey spaces, L(p,phi)(R(n)), where p is an element of [1, + infinity) and phi is the suitable doubling and integral functions.

• 出版日期2009-11
• 单位宁波大学; 浙江大学