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A Remark on Estimates for Uniformly Elliptic Operators on Weighted L p Spaces and Morrey Spaces
Author(s) -
Kurata Kazuhiro,
Sugano Satoko
Publication year - 2000
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/(sici)1522-2616(200001)209:1<137::aid-mana137>3.0.co;2-3
Subject(s) - mathematics , pure mathematics , class (philosophy) , elliptic operator , mathematical analysis , computer science , artificial intelligence
In this paper we consider uniformly elliptic operators $L= - \sum \nolimits ^n _{i, j=1} \partial _i (a _{ij} (x) \partial _j) + V(x)$ with non‐negative potentials V on ℝ n ( n ≥ 3) which belong to certain reverse Hölder class. We show several estimates for VL –1 , V 1/2 ∇ L –1 and ∇ 2 L –1 on weighted L p spaces and Morrey spaces under certain assumptions on a ij ( x ), V and p . Our results generalize some results of J. Zhong and Z. Shen in the case of L = –Δ + V ( x ) and extend to uniformly elliptic operators.