Fractional integration, Morrey spaces and a Schroedinger equation
- Univ. of Michigan, Ann Arbor, MI (United States)
Let V : R{sup 3} {yields} R be the potential for the 3-dimensional Schroedinger operator {minus}{Delta} + V. It was shown by Cwikel, Lieb and Rosenblum, [8], that the number of bound states, N(V), of {minus}{Delta} + V is bounded by N(V) {le} C {integral}{sub R3} {vert_bar}V(x){vert_bar}{sup 3/2}dx. Later Fefferman and phong, [4], improved on this inequality. Make a dyadic decomposition of R{sup 3} into cubes. Define a dyadic cube Q to be minimal with respect to {epsilon} > 0 if {integral}{sub q}{vert_bar}V(x){vert_bar}{sup p} dx {ge} {epsilon}{sup p}{vert_bar}Q{vert_bar}{sup 1-2p/3} and {integral}{sub Q}{prime} {vert_bar}V(x){vert_bar}{sup p} dx < {epsilon}{sup p}{vert_bar}Q{prime}{vert_bar}{sup 1-2p/3} for all dyadic cubes Q{prime} {contained_in} Q. 10 refs., 4 figs., 1 tab.
- Sponsoring Organization:
- USDOE
- OSTI ID:
- 482478
- Journal Information:
- Communications in Partial Differential Equations, Journal Name: Communications in Partial Differential Equations Journal Issue: 11-12 Vol. 20; ISSN CPDIDZ; ISSN 0360-5302
- Country of Publication:
- United States
- Language:
- English
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