SOME ESTIMATES FOR SCHRODINGER TYPE OPERATORS ON MUSIELAK-ORLICZ-HARDY SPACES

作者：Yang, Sibei^*

来源：Taiwanese Journal of Mathematics, 2014, 18(4): 1293-1328.

DOI：10.11650/tjm.18.2014.3897

• Musielak-Orlicz-Hardy space
• Schrodinger type operator
• Lusin area function
• Atom
• Second order Riesz transform
• Fundamental solution

Let L := -div(A del) + V be a Schrodinger type operator with the nonnegative potential V belonging to the reverse Holder class RHqo(R-n) for some q(0) is an element of [n, infinity) with n >= 3, where A satisfies the uniformly elliptic condition. Assume that phi : R-n x [0, infinity) -> [0, infinity) is a function such that phi(x,.) is an Orlicz function, phi(.,t) is an element of A(infinity) (R-n) (the class of uniformly Muckenhoupt weights) and its uniformly critical lower type index i(phi) is an element of(n/n+alpha(0), 1], where alpha(0) is an element of (0, 1] measures the regularity of kernels of the semigroup generalized by L-0 := -div(A del). In this article, we first prove that operators VL-1, V-1/2 del L-1 and del L-2(-1) are bounded from the Musielak-Orlicz-Hardy space associated with L, H-phi, L (R-n), to the Musielak-Orlicz space L-phi (R-n). Moreover, we also obtain the boundedness of .VL-1 and del L-2(-1) on H-phi, L(R-n). All these results are new even when phi(x, t) := t(p), with p is an element of(n/n+alpha(0), 1], for all x is an element of R-n and t is an element of [0, infinity).

• 出版日期2014-8
• 单位兰州大学