A Characterization of Hardy Spaces Associated with Certain Schrodinger Operators

作者：Dziubanski Jacek^*; Zienkiewicz Jacek

来源：Potential Analysis, 2014, 41(3): 917-930.

DOI：10.1007/s11118-014-9400-2

• Hardy spaces
• Schrodinger operators

Let {K (t) } (t > 0) be the semigroup of linear operators generated by a Schrodinger operator -L = Delta - V (x) on a"e (d) , d a parts per thousand yen 3, where V (x) a parts per thousand yen 0 satisfies Delta (-1) V a L (a). We say that an L (1)-function f belongs to the Hardy space if the maximal function a"(3) (L) f (x) = sup (t > 0) |K (t) f (x)| belongs to L (1) (a"e (d) ). We prove that the operator (-Delta)(1/2) L (-1/2) is an isomorphism of the space with the classical Hardy space H (1)(a"e (d) ) whose inverse is L (1/2)(-Delta)(-1/2). As a corollary we obtain that the space is characterized by the Riesz transforms R-j = partial derivative/partial derivative x(j)L(-1/2).

• 出版日期2014-10