In this paper,the authors establish the two-weight boundedness of the local fractional maximal operators and local fractional integrals on Gaussian measure spaces associated with the local weights.More precisely,the a...In this paper,the authors establish the two-weight boundedness of the local fractional maximal operators and local fractional integrals on Gaussian measure spaces associated with the local weights.More precisely,the authors first obtain the two-weight weak-type estimate for the locala fractional maximal operators of orderαfrom L^(p)(v)to L^(q,∞)(u)with 1≤p≤q<∞under a condition of(u,v)∈∪b>a A_(p,q,a)^(b') ,and then obtain the two-weight weak-type estimate for the local fractional integrals.In addition,the authors obtain the two-weight strong-type boundedness of the local fractional maximal operators under a condition of(u,v)∈M_(p,q,a)^(6a+9√da^2) and the two-weight strong-type boundedness of the local fractional integrals.These estimates are established by the radialization method and dyadic approach.展开更多
Let L=-Δ+V be a Schrodinger operator,whereΔis the Laplacian operator on R^(d)(d≥3),while the nonnegative potential V belongs to the reverse Holder class B_(q),q>d/2.In this paper,we study weighted compactness of...Let L=-Δ+V be a Schrodinger operator,whereΔis the Laplacian operator on R^(d)(d≥3),while the nonnegative potential V belongs to the reverse Holder class B_(q),q>d/2.In this paper,we study weighted compactness of commutators of some Schrodinger operators,which include Riesz transforms,standard Calderón-Zygmund operators and Littlewood-Paley functions.These results substantially generalize some well-known results.展开更多
基金Supported by National Natural Science Foundation of China(Grant Nos.11871452 and 12071473)Beijing Information Science and Technology University Foundation(Grant Nos.2025031)。
文摘In this paper,the authors establish the two-weight boundedness of the local fractional maximal operators and local fractional integrals on Gaussian measure spaces associated with the local weights.More precisely,the authors first obtain the two-weight weak-type estimate for the locala fractional maximal operators of orderαfrom L^(p)(v)to L^(q,∞)(u)with 1≤p≤q<∞under a condition of(u,v)∈∪b>a A_(p,q,a)^(b') ,and then obtain the two-weight weak-type estimate for the local fractional integrals.In addition,the authors obtain the two-weight strong-type boundedness of the local fractional maximal operators under a condition of(u,v)∈M_(p,q,a)^(6a+9√da^2) and the two-weight strong-type boundedness of the local fractional integrals.These estimates are established by the radialization method and dyadic approach.
基金supported by National Natural Science Foundation of China(Grant Nos.11871293,11871452,12071473,12071272)Shandong Natural Science Foundation of China(Grant No.ZR2017JL008)。
文摘Let L=-Δ+V be a Schrodinger operator,whereΔis the Laplacian operator on R^(d)(d≥3),while the nonnegative potential V belongs to the reverse Holder class B_(q),q>d/2.In this paper,we study weighted compactness of commutators of some Schrodinger operators,which include Riesz transforms,standard Calderón-Zygmund operators and Littlewood-Paley functions.These results substantially generalize some well-known results.
