Weighted Morrey Spaces Related to Certain Nonnegative Potentials and Riesz Transforms. (24th April 2019)
- Record Type:
- Journal Article
- Title:
- Weighted Morrey Spaces Related to Certain Nonnegative Potentials and Riesz Transforms. (24th April 2019)
- Main Title:
- Weighted Morrey Spaces Related to Certain Nonnegative Potentials and Riesz Transforms
- Authors:
- Wang, Hua
- Other Names:
- Ragusa Maria Alessandra Academic Editor.
- Abstract:
- Abstract : LetL = - Δ + V be a Schrödinger operator, whereΔ is the Laplacian onR d and the nonnegative potentialV belongs to the reverse Hölder classR H q forq ≥ d . The Riesz transform associated with the operatorL = - Δ + V is denoted byR = ∇ ( - Δ + V ) - 1 / 2 and the dual Riesz transform is denoted byR ⁎ = ( - Δ + V ) - 1 / 2 ∇ . In this paper, we first introduce some kinds of weighted Morrey spaces related to certain nonnegative potentials belonging to the reverse Hölder classR H q forq ≥ d . Then we will establish the mapping properties of the operatorR and its adjointR ⁎ on these new spaces. Furthermore, the weighted strong-type estimate and weighted endpoint estimate for the corresponding commutators[ b, R ] and[ b, R ⁎ ] are also obtained. The classes of weights, classes of symbol functions, and weighted Morrey spaces discussed in this paper are larger thanA p, B M O ( R d ), andL p, κ ( w ) corresponding to the classical Riesz transforms (V ≡ 0 ).
- Is Part Of:
- Journal of function spaces. Volume 2019(2019)
- Journal:
- Journal of function spaces
- Issue:
- Volume 2019(2019)
- Issue Display:
- Volume 2019, Issue 2019 (2019)
- Year:
- 2019
- Volume:
- 2019
- Issue:
- 2019
- Issue Sort Value:
- 2019-2019-2019-0000
- Page Start:
- Page End:
- Publication Date:
- 2019-04-24
- Subjects:
- Function spaces -- Periodicals
515.7305 - Journal URLs:
- https://www.hindawi.com/journals/jfs/ ↗
- DOI:
- 10.1155/2019/7057512 ↗
- Languages:
- English
- ISSNs:
- 2314-8896
- Deposit Type:
- Legaldeposit
- View Content:
- Available online (eLD content is only available in our Reading Rooms) ↗
- Physical Locations:
- British Library HMNTS - ELD Digital store
- Ingest File:
- 10391.xml