In this paper, we obtain the boundedness of the parabolic singular integral operator T with kernel in L（log L） 1/γ,（Sn- 1 ） on Triebel-Lizorkin spaces. Moreover, we prove the boundedness of a class of Marcinkiewi...In this paper, we obtain the boundedness of the parabolic singular integral operator T with kernel in L（log L） 1/γ,（Sn- 1 ） on Triebel-Lizorkin spaces. Moreover, we prove the boundedness of a class of Marcinkiewicz integrals μΩ,q （f） from ｜｜f｜｜Fp^oq（Rn） into Lp （Rn）.展开更多
Let μ be a non-negative Radon measure on Rd which only satisfies the following growth condition that there exists a positive constant C such that μ(B(x,r)) ≤ Crn?for all x∈ Rd, r > 0 and some fixed n ∈ (0,d]. ...Let μ be a non-negative Radon measure on Rd which only satisfies the following growth condition that there exists a positive constant C such that μ(B(x,r)) ≤ Crn?for all x∈ Rd, r > 0 and some fixed n ∈ (0,d]. This paper is interested in the properties of the iterated commutators of multilinear singular integral operators on Morrey spaces?.Precisely speaking, we show that the iterated commutators generated by multilinear singular integrals operators are bounded from to where (Regular Bounded Mean Oscillation space) and 1 qj ≤ pj ∞ with 1/p = 1/p1 + ... + 1/pm and 1/q = 1/q1+ ... + 1/qm.展开更多
Consider the general dispersive equation defined bywhere φ（√-△） is a pseudo-differential operator with symbol φ（｜ξ｜）. In this paper, for φ satisfying suitable growth conditions and the radial initial data ...Consider the general dispersive equation defined bywhere φ（√-△） is a pseudo-differential operator with symbol φ（｜ξ｜）. In this paper, for φ satisfying suitable growth conditions and the radial initial data f in Sobolev space, we give the local and global Lq estimate for the maximal operator S; defined by Sφf（x） = sup0〈t〈1｜St,φf（x）｜, where St,φ f is the solution of equation （＊）. These estimates imply the a.e. convergence of the solution of equation （＊）.展开更多
In this paper, the authors give the local L^2 estimate of the maximal operator S_(φ,γ)~* of the operator family {S_(t,φ,γ)} defined initially by ■which is the solution(when n = 1) of the following dispersive equa...In this paper, the authors give the local L^2 estimate of the maximal operator S_(φ,γ)~* of the operator family {S_(t,φ,γ)} defined initially by ■which is the solution(when n = 1) of the following dispersive equations(~*) along a curve γ:■where φ : R^+→R satisfies some suitable conditions and φ((-?)^(1/2)) is a pseudo-differential operator with symbol φ(|ξ|). As a consequence of the above result, the authors give the pointwise convergence of the solution(when n = 1) of the equation(~*) along curve γ.Moreover, a global L^2 estimate of the maximal operator S_(φ,γ)~* is also given in this paper.展开更多
Consider the generalized dispersive equation defined by{iδtu+Ф(√-△)u=0,(x,t)∈R^n×R,u(x,0)=f(x),F∈F(R^n),(*)whereФ(√-△)is a pseudo-differential operator with symbolФ(|ζ|).In the present paper,assuming t...Consider the generalized dispersive equation defined by{iδtu+Ф(√-△)u=0,(x,t)∈R^n×R,u(x,0)=f(x),F∈F(R^n),(*)whereФ(√-△)is a pseudo-differential operator with symbolФ(|ζ|).In the present paper,assuming thatФsatisfies suitable growth conditions and the initial data in H^s(R^n),we bound the Hausdorff dimension of the sets on which the pointwise convergence of solutions to the dispersive equations(*)fails.These upper bounds of Hausdorff dimension shall be obtained via the Kolmogorov-Seliverstov-Plessner method.展开更多
基金Supported in part by National Natural Foundation of China (Grant No. 11071250)
文摘In this paper, we obtain the boundedness of the parabolic singular integral operator T with kernel in L（log L） 1/γ,（Sn- 1 ） on Triebel-Lizorkin spaces. Moreover, we prove the boundedness of a class of Marcinkiewicz integrals μΩ,q （f） from ｜｜f｜｜Fp^oq（Rn） into Lp （Rn）.
文摘Let μ be a non-negative Radon measure on Rd which only satisfies the following growth condition that there exists a positive constant C such that μ(B(x,r)) ≤ Crn?for all x∈ Rd, r > 0 and some fixed n ∈ (0,d]. This paper is interested in the properties of the iterated commutators of multilinear singular integral operators on Morrey spaces?.Precisely speaking, we show that the iterated commutators generated by multilinear singular integrals operators are bounded from to where (Regular Bounded Mean Oscillation space) and 1 qj ≤ pj ∞ with 1/p = 1/p1 + ... + 1/pm and 1/q = 1/q1+ ... + 1/qm.
基金The authors would like to express their deep gratitude to the referees for their very careful reading. This work was supported by the National Natural Science Foundation of China （Grant Nos. 11371057, 11471033, 11571160, 11661061）, the Inner Mongolia University Scientific Research Projects （No. NJZZ16234）, and the Natural Science Foundation of Inner Mongolia （No. 2015MS0108）.
文摘Consider the general dispersive equation defined bywhere φ（√-△） is a pseudo-differential operator with symbol φ（｜ξ｜）. In this paper, for φ satisfying suitable growth conditions and the radial initial data f in Sobolev space, we give the local and global Lq estimate for the maximal operator S; defined by Sφf（x） = sup0〈t〈1｜St,φf（x）｜, where St,φ f is the solution of equation （＊）. These estimates imply the a.e. convergence of the solution of equation （＊）.
基金supported by the National Natural Science Foundation of China(Nos.11571160,11661061,11761054)the Inner Mongolia University Scientific Research Projects(Nos.NJZZ16234,NJZY17289)
文摘In this paper, the authors give the local L^2 estimate of the maximal operator S_(φ,γ)~* of the operator family {S_(t,φ,γ)} defined initially by ■which is the solution(when n = 1) of the following dispersive equations(~*) along a curve γ:■where φ : R^+→R satisfies some suitable conditions and φ((-?)^(1/2)) is a pseudo-differential operator with symbol φ(|ξ|). As a consequence of the above result, the authors give the pointwise convergence of the solution(when n = 1) of the equation(~*) along curve γ.Moreover, a global L^2 estimate of the maximal operator S_(φ,γ)~* is also given in this paper.
基金supported in part by the National Natural Science Foundation of China(Grant Nos.11661061,11761054)the Inner Mongolia University Scientific Research Projects(No.NJZY19186)the Natural Science Foundation of Inner Mongolia(No.2019MS01003).
文摘Consider the generalized dispersive equation defined by{iδtu+Ф(√-△)u=0,(x,t)∈R^n×R,u(x,0)=f(x),F∈F(R^n),(*)whereФ(√-△)is a pseudo-differential operator with symbolФ(|ζ|).In the present paper,assuming thatФsatisfies suitable growth conditions and the initial data in H^s(R^n),we bound the Hausdorff dimension of the sets on which the pointwise convergence of solutions to the dispersive equations(*)fails.These upper bounds of Hausdorff dimension shall be obtained via the Kolmogorov-Seliverstov-Plessner method.
