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In this article, we first give the $L^{p}$ boundedness of the operator $D^{2}L^{-1}$ with BMO coefficients and a potential $V$ satisfying an appropriate reverse H\"{o}lder condition, then obtain global $W^{1,2}_p$ estimates for the nondivergence parabolic operator $L$ with VMO coefficients and a potential $V$ satisfying an appropriate reverse H\"{o}lder condition.
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참고문헌 (18)
참고문헌 신청
A. Carbonaro / 2008 / Parabolic Schrodinger operators / J. Math. Anal. Appl 343 (2) : 965 ~ 974
B. Muckenhoupt / 1972 / Weighted norm inequalities for the Hardy maximal function / Trans. Amer. Math. Soc 165 : 207 ~ 226
C. Vitanza / 1993 / A new contribution to the W2,p regularity for a class of elliptic second order equations with discontinuous coefficients / Matematiche (Catania) 48 (2) :
D. Gilbarg / 1983 / Elliptic Partial Differential Equations of Second Order / Springer-Verlag
E. M. Stein / 1993 / Harmonic analysis: real variable methods orthogonality and oscillatory integrals / Princeton Univ. Press
B. Muckenhoupt / 1972 / Weighted norm inequalities for the Hardy maximal function / Trans. Amer. Math. Soc 165 : 207 ~ 226
C. Vitanza / 1993 / A new contribution to the W2,p regularity for a class of elliptic second order equations with discontinuous coefficients / Matematiche (Catania) 48 (2) :
D. Gilbarg / 1983 / Elliptic Partial Differential Equations of Second Order / Springer-Verlag
E. M. Stein / 1993 / Harmonic analysis: real variable methods orthogonality and oscillatory integrals / Princeton Univ. Press
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