In this article,we derive the Lp-boundedness of the variation operators associated with the heat semigroup which is generated by the high order Schrodinger type operator(—Δ)^2+V%2 in R%n(n≥5)with V being a nonnegat...In this article,we derive the Lp-boundedness of the variation operators associated with the heat semigroup which is generated by the high order Schrodinger type operator(—Δ)^2+V%2 in R%n(n≥5)with V being a nonnegative potential satisfying the reverse Holder inequality.Furt her more,we prove the boundedness of the variation operators on associated Morrey spaces.In the proof of the main results,we always make use of the variation inequalities associated with the hea t semigroup genera ted by the biharmonic operator(-Δ)2.展开更多
. Let H2 = （-△）2 ＋ V2 be the Schr6dinger type operator, where V satisfies reverse HSlder inequality. In this paper, we establish the Lp boundedness for V2 H2- 1, H21 V2, VH2- 1/2 and Hfl/2V, and that of their comm.... Let H2 = （-△）2 ＋ V2 be the Schr6dinger type operator, where V satisfies reverse HSlder inequality. In this paper, we establish the Lp boundedness for V2 H2- 1, H21 V2, VH2- 1/2 and Hfl/2V, and that of their commutators. We also prove that H^IV2, Hfl/2V are bounded from BMOL to BMOL.展开更多
基金supported by the National Natural Science Foundation of China(11701453)Fundamental Research Funds for the Central Universities(31020180QD05)+2 种基金The second author was supported by the National Natural Science Foundation of China(11971431,11401525)the Natural Science Foundation of Zhejiang Province(LY18A010006)and the first Class Discipline of Zhejiang-A(Zhejiang Gongshang University-Statistics).
文摘In this article,we derive the Lp-boundedness of the variation operators associated with the heat semigroup which is generated by the high order Schrodinger type operator(—Δ)^2+V%2 in R%n(n≥5)with V being a nonnegative potential satisfying the reverse Holder inequality.Furt her more,we prove the boundedness of the variation operators on associated Morrey spaces.In the proof of the main results,we always make use of the variation inequalities associated with the hea t semigroup genera ted by the biharmonic operator(-Δ)2.
基金Supported by the National Natural Science Foundation of China(11261023,11401269,11461033)the Natural Science Foundation of Jiangxi Province(20142BAB201003)
文摘. Let H2 = （-△）2 ＋ V2 be the Schr6dinger type operator, where V satisfies reverse HSlder inequality. In this paper, we establish the Lp boundedness for V2 H2- 1, H21 V2, VH2- 1/2 and Hfl/2V, and that of their commutators. We also prove that H^IV2, Hfl/2V are bounded from BMOL to BMOL.
