Weighted Morrey Spaces Related to Schrödinger Operators with Nonnegative Potentials and Fractional Integrals
Let ℒ=−Δ+V be a Schrödinger operator on ℝd, d≥3, where Δ is the Laplacian operator on ℝd, and the nonnegative potential V belongs to the reverse Hölder class RHs with s≥d/2. For given 0<α<d, the fractional integrals associated with the Schrödinger operator ℒ is defined by ℐα=ℒ−α/2. Suppose tha...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2020-01-01
|
| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2020/6907170 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832546917116018688 |
|---|---|
| author | Hua Wang |
| author_facet | Hua Wang |
| author_sort | Hua Wang |
| collection | DOAJ |
| description | Let ℒ=−Δ+V be a Schrödinger operator on ℝd, d≥3, where Δ is the Laplacian operator on ℝd, and the nonnegative potential V belongs to the reverse Hölder class RHs with s≥d/2. For given 0<α<d, the fractional integrals associated with the Schrödinger operator ℒ is defined by ℐα=ℒ−α/2. Suppose that b is a locally integrable function on ℝd and the commutator generated by b and ℐα is defined by b.ℐαfx=bx⋅ℐαfx−ℐαbfx. In this paper, we first introduce some kinds of weighted Morrey spaces related to certain nonnegative potentials belonging to the reverse Hölder class RHs with s≥d/2. Then, we will establish the boundedness properties of the fractional integrals ℐα on these new spaces. Furthermore, weighted strong-type estimate for the corresponding commutator b,ℐα in the framework of Morrey space is also obtained. The classes of weights, the classes of symbol functions, as well as weighted Morrey spaces discussed in this paper are larger than Ap,q, BMOℝd, and Lp,κμ,ν corresponding to the classical case (that is V≡0). |
| format | Article |
| id | doaj-art-f9d745ffc0b549e28282e01a9bcd26f6 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-f9d745ffc0b549e28282e01a9bcd26f62025-02-03T06:46:53ZengWileyJournal of Function Spaces2314-88962314-88882020-01-01202010.1155/2020/69071706907170Weighted Morrey Spaces Related to Schrödinger Operators with Nonnegative Potentials and Fractional IntegralsHua Wang0School of Mathematics and Systems Science, Xinjiang University, Urumqi 830046, ChinaLet ℒ=−Δ+V be a Schrödinger operator on ℝd, d≥3, where Δ is the Laplacian operator on ℝd, and the nonnegative potential V belongs to the reverse Hölder class RHs with s≥d/2. For given 0<α<d, the fractional integrals associated with the Schrödinger operator ℒ is defined by ℐα=ℒ−α/2. Suppose that b is a locally integrable function on ℝd and the commutator generated by b and ℐα is defined by b.ℐαfx=bx⋅ℐαfx−ℐαbfx. In this paper, we first introduce some kinds of weighted Morrey spaces related to certain nonnegative potentials belonging to the reverse Hölder class RHs with s≥d/2. Then, we will establish the boundedness properties of the fractional integrals ℐα on these new spaces. Furthermore, weighted strong-type estimate for the corresponding commutator b,ℐα in the framework of Morrey space is also obtained. The classes of weights, the classes of symbol functions, as well as weighted Morrey spaces discussed in this paper are larger than Ap,q, BMOℝd, and Lp,κμ,ν corresponding to the classical case (that is V≡0).http://dx.doi.org/10.1155/2020/6907170 |
| spellingShingle | Hua Wang Weighted Morrey Spaces Related to Schrödinger Operators with Nonnegative Potentials and Fractional Integrals Journal of Function Spaces |
| title | Weighted Morrey Spaces Related to Schrödinger Operators with Nonnegative Potentials and Fractional Integrals |
| title_full | Weighted Morrey Spaces Related to Schrödinger Operators with Nonnegative Potentials and Fractional Integrals |
| title_fullStr | Weighted Morrey Spaces Related to Schrödinger Operators with Nonnegative Potentials and Fractional Integrals |
| title_full_unstemmed | Weighted Morrey Spaces Related to Schrödinger Operators with Nonnegative Potentials and Fractional Integrals |
| title_short | Weighted Morrey Spaces Related to Schrödinger Operators with Nonnegative Potentials and Fractional Integrals |
| title_sort | weighted morrey spaces related to schrodinger operators with nonnegative potentials and fractional integrals |
| url | http://dx.doi.org/10.1155/2020/6907170 |
| work_keys_str_mv | AT huawang weightedmorreyspacesrelatedtoschrodingeroperatorswithnonnegativepotentialsandfractionalintegrals |