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Let 0<β<1 andΩbe a proper open and non-empty subset of Rn.In this paper,the object of our investigation is the multilinear local maximal operator Mβ,defined by Mβ((f))(x)=supQ(∈xQ∈Fβ)Πi=1^m1/|Q|∫Q|fi(yi)|dyi,where Fβ={Q(x,l):x∈Ω,l<βd(x,Ωc)},Q=Q(x,l)is denoted as a cube with sides parallel to the axes,and x and l denote its center and half its side length.Two-weight characterizations for the multilinear local maximal operator Mβare obtained.A formulation of the Carleson embedding theorem in the multilinear setting is proved. 相似文献
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潘亚丽 《数学物理学报(B辑英文版)》2023,(5):2309-2319
Let L be the Laplace-Beltrami operator.On an n-dimensional(n≥ 2),complete,noncompact Riemannian manifold M,we prove that if 0 <α <1,s> α/2 and f ∈ Hs(M),then the fractional Schr?dinger propagator e(it|L|α/2)(f)(x)→f(x) a.e.as t→0.In addition,for when M is a Lie group,the rate of the convergence is also studied.These results are a non-trivial extension of results on Euclidean spaces and compact manifolds. 相似文献
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