In this paper, we discuss the multilinear commutator of θ-type Calderón- Zygmund operators, and obtain that this kind of multilinear commutators is bounded from Lp(Rn) to Lq(Rn), from Lp(Rn) to Triebel-Lizorkin ...In this paper, we discuss the multilinear commutator of θ-type Calderón- Zygmund operators, and obtain that this kind of multilinear commutators is bounded from Lp(Rn) to Lq(Rn), from Lp(Rn) to Triebel-Lizorkin spaces and on certain Hardy type spaces.展开更多
Our aim in the present paper is to prove the boundedness of commutators on Morrey spaces with variable exponent. In order to obtain the result, we clarify a relation between variable exponent and BMO norms.
In this paper, we will prove the boundedness of Hardy type operators Hβ(x) and H*β(x) of variable order β(x) on Herz spaces Kα(·)p(·),q and Kα(·)p(·),q' where α(·) and p(·)are b...In this paper, we will prove the boundedness of Hardy type operators Hβ(x) and H*β(x) of variable order β(x) on Herz spaces Kα(·)p(·),q and Kα(·)p(·),q' where α(·) and p(·)are both variable.展开更多
In this paper, the boundedness in Lebesgue spaces of commutators and multilinear commutators generated by θ-type Calderón-Zygmund operators with RB MO(μ) functions on non-homogeneous metric measure spaces is ob...In this paper, the boundedness in Lebesgue spaces of commutators and multilinear commutators generated by θ-type Calderón-Zygmund operators with RB MO(μ) functions on non-homogeneous metric measure spaces is obtained.展开更多
In this paper, we will use a method of sharp maximal function approach to show the boundedness of commutator [b,TδR] by Bochner-Riesz operators and the function b on weighted Morrey spaces Lp,κ(ω) under appropriate...In this paper, we will use a method of sharp maximal function approach to show the boundedness of commutator [b,TδR] by Bochner-Riesz operators and the function b on weighted Morrey spaces Lp,κ(ω) under appropriate conditions on the weight ω, where b belongs to Lipschitz space or weighted Lipschitz space.展开更多
[b,T] denotes the commutator of generalized Calderon-Zygmund operators T with Lipschitz function b, where b∈Lip_β(R^n),(0 <β≤1) and T is aθ(t)-type Calderón-Zygmund operator. The commutator [b,T] generate...[b,T] denotes the commutator of generalized Calderon-Zygmund operators T with Lipschitz function b, where b∈Lip_β(R^n),(0 <β≤1) and T is aθ(t)-type Calderón-Zygmund operator. The commutator [b,T] generated by b and T is defined by[b,T]f(x)=b(x)Tf(x)-T(bf)(x)=∫k(x,y)(b(x)-b(y))f(y)dy.In this paper, the authors discuss the boundedness of the commutator [b, T] on weighted Hardy spaces and weighted Herz type Hardy spaces and prove that [b,T] is bounded from H^p(ω~p) to L^q(ω~q), and from HK_(q1)^(α,p)(ω_1,ω_2^(q1)) to K_(q2)^(α,p)(ω_1,ω_2^(q2)). The results extend and generalize the well-known ones in [7].展开更多
基金NSF of Anhui Province (No.07021019)Education Committee of Anhui Province (No.KJ2007A009)NSF of Chaohu College(No. XLY-200823)
文摘In this paper, we discuss the multilinear commutator of θ-type Calderón- Zygmund operators, and obtain that this kind of multilinear commutators is bounded from Lp(Rn) to Lq(Rn), from Lp(Rn) to Triebel-Lizorkin spaces and on certain Hardy type spaces.
基金supported by NSFC (No. 11101001 and No. 11201003)Education Committee of Anhui Province (No. KJ2011A138 and No. KJ2012A133)
文摘Our aim in the present paper is to prove the boundedness of commutators on Morrey spaces with variable exponent. In order to obtain the result, we clarify a relation between variable exponent and BMO norms.
基金supported by NSFC (No. 11201003)Education Committee of Anhui Province (No. KJ2012A133)
文摘In this paper, we will prove the boundedness of Hardy type operators Hβ(x) and H*β(x) of variable order β(x) on Herz spaces Kα(·)p(·),q and Kα(·)p(·),q' where α(·) and p(·)are both variable.
基金supported by NSF of Anhui Province(No.1608085QA12)NSF of Education Committee of Anhui Province(Nos.KJ2016A506 and KJ2017A454)+2 种基金Excellent Young Talents Foundation of Anhui Province(No.GXYQ2017070)Doctoral Scientific Research Foundation of Chaohu University(No.KYQD-201605)Scientific Research Project of Chaohu University(No.XLY-201501)
文摘In this paper, the boundedness in Lebesgue spaces of commutators and multilinear commutators generated by θ-type Calderón-Zygmund operators with RB MO(μ) functions on non-homogeneous metric measure spaces is obtained.
基金supported by NSFC (NO. 11201003)Education Committee of Anhui Province (NO. KJ2011A138 and NO. KJ2012A133)
文摘In this paper, we will use a method of sharp maximal function approach to show the boundedness of commutator [b,TδR] by Bochner-Riesz operators and the function b on weighted Morrey spaces Lp,κ(ω) under appropriate conditions on the weight ω, where b belongs to Lipschitz space or weighted Lipschitz space.
文摘[b,T] denotes the commutator of generalized Calderon-Zygmund operators T with Lipschitz function b, where b∈Lip_β(R^n),(0 <β≤1) and T is aθ(t)-type Calderón-Zygmund operator. The commutator [b,T] generated by b and T is defined by[b,T]f(x)=b(x)Tf(x)-T(bf)(x)=∫k(x,y)(b(x)-b(y))f(y)dy.In this paper, the authors discuss the boundedness of the commutator [b, T] on weighted Hardy spaces and weighted Herz type Hardy spaces and prove that [b,T] is bounded from H^p(ω~p) to L^q(ω~q), and from HK_(q1)^(α,p)(ω_1,ω_2^(q1)) to K_(q2)^(α,p)(ω_1,ω_2^(q2)). The results extend and generalize the well-known ones in [7].
