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1.
Our first aim in this paper is to prove boundedness of commutators with fractional integrals on Lebesgue spaces with variable exponent. We additionally obtain the boundedness on Herz spaces with variable exponent applying some properties of variable exponent and BMO norms.  相似文献   

2.
A class of anisotropic Herz-type Hardy spaces with variable exponent associated with a non-isotropic dilation on \({\mathbb{R}^{n}}\) are introduced, and characterizations of these spaces are established in terms of atomic and molecular decompositions. As some applications of the decomposition theory, the authors study the interpolation problem and the boundedness of a linear operator on the anisotropic Herz-type Hardy spaces with variable exponent.  相似文献   

3.
4.
Let \({M_\beta }\) be the fractional maximal function. The commutator generated by \({M_\beta }\) and a suitable function b is defined by \([{M_\beta },b]f = {M_\beta }(bf) - b{M_\beta }(f)\) . Denote by P(? n ) the set of all measurable functions p(·): ? n → [1,∞) such that $1 < p_ - : = \mathop {es\sin fp(x)}\limits_{x \in \mathbb{R}^n } andp_ + : = \mathop {es\operatorname{s} \sup p(x) < \infty }\limits_{x \in \mathbb{R}^n } ,$ and by B(? n ) the set of all p(·) ∈ P(? n ) such that the Hardy-Littlewood maximal function M is bounded on L p(·)(? n ). In this paper, the authors give some characterizations of b for which \([{M_\beta },b]\) is bounded from L p(·)(? n ) into L q(·)(? n ), when p(·) ∈ P(? n ), 0 < β < n/p + and 1/q(·) = 1/p(·) ? β/n with q(·)(n ? β)/nB(? n ).  相似文献   

5.
LetT Ω,α (0 ≤ α< n) be the singular and fractional integrals with variable kernel Ω(x, z), and [b, TΩ,α] be the commutator generated by TΩ,α and a Lipschitz functionb. In this paper, the authors study the boundedness of [b, TΩ,α] on the Hardy spaces, under some assumptions such as theL r -Dini condition. Similar results and the weak type estimates at the end-point cases are also given for the homogeneous convolution operators . The smoothness conditions imposed on are weaker than the corresponding known results.  相似文献   

6.
Commutators of singular integrals on spaces of homogeneous type   总被引:1,自引:0,他引:1  
In this work we prove some sharp weighted inequalities on spaces of homogeneous type for the higher order commutators of singular integrals introduced by R. Coifman, R. Rochberg and G. Weiss in Factorization theorems for Hardy spaces in several variables, Ann. Math. 103 (1976), 611–635. As a corollary, we obtain that these operators are bounded on L p (w) when w belongs to the Muckenhoupt’s class A p , p > 1. In addition, as an important tool in order to get our main result, we prove a weighted Fefferman-Stein type inequality on spaces of homogeneous type, which we have not found previously in the literature.  相似文献   

7.
In this paper,the authors study the boundedness of the operator μ b Ω,the commutator generated by a function b ∈Lip β (R n)(0 < β < 1) and the Marcinkiewicz integral μΩ on weighted Herz-type Hardy spaces.  相似文献   

8.
In this paper, the authors investigate the boundedness of the generalized fractional integrals of Pérez on the weighted Herz spaces, the weighted weak Herz spaces and the weighted Herz-type Hardy spaces for general weights. This project was partially supported by the SEDF and the NNSF of China.  相似文献   

9.
In this paper, the authors investigate the boundedness of the generalized fractional integrals of Pérez on the weighted Herz spaces, the weighted weak Herz spaces and the weighted Herz-type Hardy spaces for general weights.  相似文献   

10.
利用加权Herz型Hardy空间的原子分解理论,讨论了广义分数次积分算子Tl从加权Lp空间到加权Lq空间,以及从加权Herz型Hardy空间到加权Herz空间的有界性问题.将已有的分数次积分算子的结论推广到广义分数次积分算子的情形.  相似文献   

11.
In this paper the boundedness properties of multilinear singular and fractional integrals on the weighted Hardy spaces are studied.  相似文献   

12.
Let μ be a Borel measure on Rd which may be non doubling. The only condition that μ must satisfy is μ(Q) ≤ col(Q)n for any cube Q () Rd with sides parallel to the coordinate axes and for some fixed n with 0 < n ≤ d. The purpose of this paper is to obtain a boundedness property of fractional integrals in Hardy spaces H1 (μ).  相似文献   

13.
Periodica Mathematica Hungarica - We establish an interpolation result for the rearrangement-invariant martingale Hardy spaces. By using this interpolation result, we extend the mapping properties...  相似文献   

14.
Let T be the multiplier operator associated to a multiplier m, and [b, T] be the commutator generated by T and a BMO function b. In this paper, the authors have proved that [b,T] is bounded from the Hardy space H^1(R^n) into the weak L^1 (R^n) space and from certain atomic Hardy space Hb^1 (R^n) into the Lebesgue space L^1 (R^n), when the multiplier m satisfies the conditions of Hoermander type.  相似文献   

15.
设TΩ,α是带变量核Ω的分数次积分算子,通过加强核的条件,并利用Hardy空间的原子分解技术,建立了TΩ,α(0<α<n)从Hardy空间到Lq(Rn)空间的有界性.推广了相关文献的结论.  相似文献   

16.
In this paper, we prove a necessary and sufficiency condition for the weighted Hardy operator
Hυ,ωf(x)=υ(x)0xf(t)ω(t)dt
to be compactly acting from Lp(?)(0,) to Lq(?)(0,).  相似文献   

17.
A molecular characterization of the weighted Herz-type Hardy spaces and is given, by which the boundedness of the Hilbert transform and the Riesz transforms are proved on these space for 0<p1. These results are obtained by first deriving that the convolution operator Tf=k*f is bounded on the weighted Herz-type Hardy spaces.  相似文献   

18.
本文证明了多线性分数次Hardy算子Hβ,m和H *β,m (m∈Z+且m≥1)在变指数Herz-Morrey乘积空间上的有界性.对多线性Hardy算子也建立了相应的结果.  相似文献   

19.
Boundedness of multilinear singular integrals and their commutators from products of variable exponent Lebesgue spaces to variable exponent Lebesgue spaces are obtained. The vector-valued case is also considered.  相似文献   

20.
通过放宽尺寸条件,得到了一类具有分数次积分性质的次线性算子从Herz型Hardy空间到(弱)Herz型Hardy空间有界性的判定条件,以及端点处的弱型估计.  相似文献   

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