119 research outputs found

    Some estimates of intrinsic square functions on weighted Herz-type Hardy spaces

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    In this paper, by using the atomic decomposition theory of weighted Herz-type Hardy spaces, we will obtain some strong type and weak type estimates for intrinsic square functions including the Lusin area function, Littlewood-Paley G\mathcal G-function and Gλ∗\mathcal G^*_\lambda-function on these spaces.Comment: 25 pages. arXiv admin note: substantial text overlap with arXiv:1210.5795, arXiv:1010.0862, arXiv:1009.6142, arXiv:1102.4380, arXiv:1111.1387, arXiv:1103.171

    Boundedness for fractional Hardy-type operator on Herz-Morrey spaces with variable exponent

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    In this paper, the fractional Hardy-type operator of variable order β(x)\beta(x) is shown to be bounded from the Herz-Morrey spaces MK˙p1,q1(⋅)α,λ(Rn)M\dot{K}_{p_{_{1}},q_{_{1}}(\cdot)}^{\alpha,\lambda}(\mathbb{R}^{n}) with variable exponent q1(x)q_{1}(x) into the weighted space MK˙p2,q2(⋅)α,λ(Rn,ω)M\dot{K}_{p_{_{2}},q_{_{2}}(\cdot)}^{\alpha,\lambda}(\mathbb{R}^{n},\omega), where ω=(1+∣x∣)−γ(x)\omega=(1+|x|)^{-\gamma(x)} with some γ(x)>0\gamma(x)>0 and 1/q1(x)−1/q2(x)=β(x)/n 1/q_{_{1}}(x)-1/q_{_{2}}(x)=\beta(x)/n when q1(x)q_{_{1}}(x) is not necessarily constant at infinity. It is assumed that the exponent q1(x)q_{_{1}}(x) satisfies the logarithmic continuity condition both locally and at infinity that 1<q1(∞)≤q1(x)≤(q1)+<∞ (x∈Rn)1< q_{1}(\infty)\le q_{1}(x)\le( q_{1})_{+}<\infty~(x\in \mathbb{R}^{n}).Comment: 13 page

    Boundedness for fractional Hardy-type operator on variable exponent Herz-Morrey spaces

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    In this paper, the fractional Hardy-type operator of variable order β(x)\beta(x) is shown to be bounded from the variable exponent Herz-Morrey spaces MK˙p1,q1(⋅)α(⋅),λ(Rn)M\dot{K}_{p_{_{1}},q_{_{1}}(\cdot)}^{\alpha(\cdot),\lambda}(\R^{n}) into the weighted space MK˙p2,q2(⋅)α(⋅),λ(Rn,ω)M\dot{K}_{p_{_{2}},q_{_{2}}(\cdot)}^{\alpha(\cdot),\lambda}(\R^{n},\omega), where α(x)∈L∞(Rn)\alpha(x)\in L^{\infty}(\mathbb{R}^{n}) be log-H\"older continuous both at the origin and at infinity, ω=(1+∣x∣)−γ(x)\omega=(1+|x|)^{-\gamma(x)} with some γ(x)>0\gamma(x)>0 and 1/q1(x)−1/q2(x)=β(x)/n 1/q_{_{1}}(x)-1/q_{_{2}}(x)=\beta(x)/n when q1(x)q_{_{1}}(x) is not necessarily constant at infinity.Comment: 14 pages, Kyoto J. Math.(In Press). arXiv admin note: substantial text overlap with arXiv:1404.163

    Spectra of Bochner-Riesz means on LpL^p

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    The Bochner-Riesz means are shown to have either the unit interval [0,1][0,1] or the whole complex plane as their spectra on $L^p, 1\le p<\infty

    Fractional integrals and Fourier transforms

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    This paper gives a short survey of some basic results related to estimates of fractional integrals and Fourier transforms. It is closely adjoint to our previous survey papers \cite{K1998} and \cite{K2007}. The main methods used in the paper are based on nonincreasing rearrangements. We give alternative proofs of some results. We observe also that the paper represents the mini-course given by the author at Barcelona University in October, 2014.Comment: 42 page

    Commutators of integral operators with variable kernels on Hardy spaces

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    Let \T (0\leq \alpha be the singular and fractional integrals with variable kernel Ω(x,z)\Omega(x,z), and [b,\T] be the commutator generated by \T and a Lipschitz function bb. In this paper, the authors study the boundedness of [b,\T] on the Hardy spaces, under some assumptions such as the LrL^r-Dini condition. Similar results and the weak type estimates at the end-point cases are also given for the homogeneous convolution operators \tT (0\leq \alpha . The smoothness conditions imposed on \tOmega are weaker than the corresponding known results.Comment: 12 page

    Multilinear Hausdorff operators on some function spaces with variable exponent

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    The aim of the present paper is to give necessary and sufficient conditions for the boundedness of a general class of multilinear Hausdorff operators that acts on the product of some weighted function spaces with variable exponent such as the weighted Lebesgue, Herz, central Morrey and Morrey-Herz type spaces with variable exponent. Our results improve and generalize some previous known results.Comment: 36 page

    Weighted norm inequalities for rough Hausdorff operator and its commutators on the Heisenberg group

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    The aim of this paper is to study the sharp bounds of rough Hausdorff operators on the product of Herz, central Morrey and Morrey-Herz spaces with both power weights and Muckenhoupt weights on the Heisenberg group. Especially, by applying the block decomposition of the Herz space, we obtain the boundedness of rough Hausdorff operator in the case 0 < p < 1. In addition, the boundedness for the commutators of rough Hausdorff operators on such spaces with symbols in weighted central BMO space is also established.Comment: added Nguyen Minh Chuong as the first autho

    Average operators on rectangular Herz spaces

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    We introduce a family or Herz type spaces considering rectangles instead of balls and we study continuity properties of some average operators acting on themComment: 11 page

    Mixed means of commutators of central integral means and CMO

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    In this paper we obtain some mixed means and weighted LpL^p estimates for the commutators generating rr order central integral means operators with CMOCMO functions.Comment: 9 page
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