Sign-changing Solutions to Nonlinear Elliptic Equations with Hardy Potential and Critical Parameter in ℝ2

Acta Mathematicae Applicatae Sinica, English Series - In this paper, a new Hilbert space is defined which is embedded into $$W_{0}^{1, q}(\Omega)$$ for 1 ≤ q < 2. By using...     

Two New Lipschitz Type Spaces and Their Characterizations

Acta Mathematica Sinica, English Series - In this paper, we first introduce the weak Lipschitz spaces WLipq,α, 1 < q < ∞, 0 < α < 1 which are the analog...     

Multipliers and Morrey Spaces

We study the pointwise multipliers from one Morrey space to another Morrey space. We give a necessary and sufficient condition to grant that the space of those multipliers is a Morrey space as well.     

New Characterizations of the Dual Spaces of Hardy-amalgam Spaces

Acta Mathematica Sinica, English Series - In this paper, carrying on with our study of the Hardy-amalgam spaces $${{\cal H}^{(q,p)}}$$ and $${\cal H}_{{\rm{loc}}}^{(q,p)}$$ (0 < q, p...     

非齐型空间上分数型Marcinkiewicz积分算子的加权估计

令（X，d，μ）为满足所谓上倍双倍条件和几何双倍条件的度量测度空间.设M_β，ρ，q为（X，d，μ）上的分数型Marcinkiewicz积分算子.在本文中，作者证明了若β ∈[0，∞），ρ ∈（0，∞），q ∈（1，∞）且M_β，ρ，q在L²（μ）上有界，则M_β，ρ，q是从加权Lebesgue空间L^p（w）到加权弱Lebesgue空间L^p，∞（w）上有界和从加权Morrey空间L^p，κ，η（ω）到加权弱Morrey空间WL^p，κ，η（ω）上有界.     

Finite Atomic Decomposition Characterization of Variable Anisotropic Hardy Spaces

Acta Mathematica Sinica, English Series - In 2011, Dekel et al. developed highly geometric Hardy spaces Hp(Θ), for the full range 0 < p ≤ 1, which are constructed by continuous...     

分数次积分交换子在非齐Morrey空间上的紧性

The aim of this paper is to establish the necessary and sufficient conditions for the compactness of fractional integral commutator[b,I_γ]which is generated by fractional integral I_γand function b∈Lip_β(μ)on Morrey space over non-homogeneous metric measure space,which satisfies the geometrically doubling and upper doubling conditions in the sense of Hytonen.Under assumption that the dominating functionλsatisfies weak reverse doubling condition,the author proves that the commutator[b,I_γ]is compact from Morrey space M_q^p(μ)into Morrey space M_t^s(μ)if and only if b∈Lip_β(μ).     

Bounded Gaps between Primes of Special Form

Doklady Mathematics - Let 0 < α, σ < 1 be arbitrary fixed constants, let $${{q}_{1}} < {{q}_{2}} < \ldots < {{q}_{n}} < {{q}_{{n + 1}}}$$...     

New a Priori Estimates for q-Nonlinear Elliptic Systems with Strong Nonlinearities in the Gradient, 1<q<2

We consider q-nonlinear nondiagonal elliptic systems, where 1 < q < 2, with strong nonlinear terms in the gradient. Under a smallness condition on the gradient of a solution in the Morrey space L^q,n−q, we estimate the L^p-norm of the gradient for p > q and the Holder norm of the solution for the case n = 2. An abstract theorem on “quasireverse Holder inequalities” proved by the author earlier is used essentially. Bibliography: 24 titles. Dedicated to N. N. Uraltseva on the occasion of her 70th birthday __________ Published in Zapiski Nauchnykh Seminarov POMI, Vol. 310, 2004, pp. 19–48.     

与截面相关的Morrey空间与奇异积分

In this paper, we define the Morrey spaces M_F~(p,q) (Rn) and the Campanato spaces E_F~(p,q) (R~n) associated with a family F of sections and a doubling measure μ, where F is closely related to the Monge-Amp`ere equation. Furthermore, we obtain the boundedness of the Hardy-Littlewood maximal function associated to F, Monge-Amp`ere singular integral operators and fractional integrals on M_F~(p,q)(R~n). We also prove that the Morrey spaces M_F~(p,q) (R~n)and the Campanato spaces E_F~(p,q) (R~n) are equivalent with 1 ≤ q ≤ p ∞.     

几类具有粗糙核的算子在加权Morrey空间上的有界性

设Ω∈L~q(S~(n-1))且1相似文献   

New Characterizations of Besov-Triebel-Lizorkin-Hausdorff Spaces Including Coorbits and Wavelets

In this paper, the authors establish new characterizations of the recently introduced Besov-type spaces $\dot{B}^{s,\tau}_{p,q}({\mathbb{R}}^{n})$ and Triebel-Lizorkin-type spaces $\dot{F}^{s,\tau}_{p,q}({\mathbb{R}}^{n})$ with p∈(0,∞], s∈?, τ∈[0,∞), and q∈(0,∞], as well as their preduals, the Besov-Hausdorff spaces $B\!\dot{H}^{s,\tau}_{p,q}({\mathbb{R}}^{n})$ and Triebel-Lizorkin-Hausdorff spaces $F\!\dot{H}^{s,\tau}_{p,q}({\mathbb{R}}^{n})$ , in terms of the local means, the Peetre maximal function of local means, and the tent space (the Lusin area function) in both discrete and continuous types. As applications, the authors then obtain interpretations as coorbits in the sense of Rauhut (Stud. Math. 180:237–253, 2007) and discretizations via biorthogonal wavelet bases for the full range of parameters of these function spaces. Even for some special cases of this setting such as $\dot{F}^{s}_{\infty,q}({\mathbb{R}}^{n})$ for s∈?, q∈(0,∞] (including ?BMO(? ⁿ ) when s=0 and q=2), the Q space Q _α (? ⁿ ), the Hardy-Hausdorff space HH _?α (? ⁿ ) for α∈(0,min{n/2,1}), the Morrey space ${\mathcal{M}}^{u}_{p}({\mathbb{R}}^{n})$ for 1<p≤u<∞, and the Triebel-Lizorkin-Morrey space $\dot{\mathcal{E}}^{s}_{upq}({\mathbb{R}}^{n})$ for 0<p≤u<∞, s∈? and q∈(0,∞], some of these results are new.     

Boundedness of the fractional maximal operator in generalized Morrey space on the Heisenberg group

In this paper we study the fractional maximal operator M _α , 0 ≤ α < Q on the Heisenberg group ? _n in the generalized Morrey spaces M _{p, ?}(? _n ), where Q = 2n + 2 is the homogeneous dimension of ? _n . We find the conditions on the pair (? ₁, ? ₂) which ensures the boundedness of the operator M _α from one generalized Morrey space M _{p, ?1}(? _n ) to another M _{q, ?2}(? _n ), 1 < p < q < ∞, 1/p?1/q = α/Q, and from the space M _{1, ?1}(? _n ) to the weak space WM _{q, ?2}(? _n ), 1 < q < ∞, 1 ? 1/q = α/Q. We also find conditions on the φ which ensure the Adams type boundedness of M _α from $M_{p,\phi ^{\tfrac{1} {p}} } \left( {\mathbb{H}_n } \right)$ to $M_{q,\phi ^{\tfrac{1} {q}} } \left( {\mathbb{H}_n } \right)$ for 1 < p < q < ∞ and from M _{1, ?}(? _n ) to $WM_{q,\phi ^{\tfrac{1} {q}} } \left( {\mathbb{H}_n } \right)$ for 1 < q < ∞. As applications we establish the boundedness of some Schrödinger type operators on generalized Morrey spaces related to certain nonnegative potentials V belonging to the reverse Hölder class B _∞(” _n ).     

Strongly Singular Calderon-Zygmund Operator and Commutator on Morrey Type Spaces

In this paper, the author considers the boundedness of strongly singular Calderdn Zygmund operator and commutator generated by this operator and Lipschitz function on the classical Morrey space and generalized Morrey space. Moreover, the boundedness of strongly singular Calderón- Zygmund operator on the predual of Morrey space is discussed.     

On a certain set of Lerch’s zeta-functions and their derivatives∗

Lithuanian Mathematical Journal - For 0 &lt; α ≤ 1 and 0 &lt; λ ≤ 1, let L(α, λ, s) denote the associated Lerch zeta-function, which is defined as $$...     

Marcinkiewicz积分交换子在Herz型空间中的弱型估计

用μΩ表示Marcinkiewicz积分,μΩ,b表示μΩ与函数b∈BMO(R~n)生成的交换子．本文证明了交换子μΩ,b是从Herz型Hardy空间H■_q~(n(1-(1/q)),p)(R~n)到弱Herz空间W■_q~(n(1-(1/q)),p)(R~n)有界的,其中0＜p≤1,1＜q＜∞．     

Morrey-Sobolev Spaces on Metric Measure Spaces

In this article, the authors introduce the Newton-Morrey-Sobolev space on a metric measure space (??, d, μ). The embedding of the Newton-Morrey-Sobolev space into the Hölder space is obtained if ?? supports a weak Poincaré inequality and the measure μ is doubling and satisfies a lower bounded condition. Moreover, in the Ahlfors Q-regular case, a Rellich-Kondrachov type embedding theorem is also obtained. Using the Haj?asz gradient, the authors also introduce the Haj?asz-Morrey-Sobolev spaces, and prove that the Newton-Morrey-Sobolev space coincides with the Haj?asz-Morrey-Sobolev space when μ is doubling and ?? supports a weak Poincaré inequality. In particular, on the Euclidean space \({\mathbb R}^n\) , the authors obtain the coincidence among the Newton-Morrey-Sobolev space, the Haj?asz-Morrey-Sobolev space and the classical Morrey-Sobolev space. Finally, when (??, d) is geometrically doubling and μ a non-negative Radon measure, the boundedness of some modified (fractional) maximal operators on modified Morrey spaces is presented; as an application, when μ is doubling and satisfies some measure decay property, the authors further obtain the boundedness of some (fractional) maximal operators on Morrey spaces, Newton-Morrey-Sobolev spaces and Haj?asz-Morrey-Sobolev spaces.     

奇异积分和位势积分交换子在极大Morrey空间上的有界性

设齐次空间(X,ρ,μ)上定义一类极大Morrey空间L~(p),θ,λ)(X,μ).此类极大Morrey空间是经典的Morrey空间和极大Lebesgue空间的推广.本文考虑了C-Z积分算子、位势算子与BMO函数生成的交换子在该类极大Morrey空间上的有界性.事实上,这些结果甚至在一般的欧式空间上也是新颖的.     

关于有界对称域上的混合范数空间

本文研究了Ｃｎ中有界对称域Ω上的混合范数空间Ｈ（ｐ，ｑ，　）其中０＜ ｐ＜　，０＜ｑ＜　，　是正规函数，给出了Ω上全纯函数ｆ的分数导数ｆ［β］和 分数积分ｆ［β］属于（ｐ，ｑ，）的等价条件。应用这些结果，就两种情形０＜ｐ≤２， ０＜ｑ＜　和２≤ｐ＜，０＜ｑ＜ ，用全纯函数ｆ的展式中的系数，分别给出了 ｆ　Ｈ（ｐ，ｑ，）的必要条件和充分条件，并证明了多调和函数ｕ组成的混合范数空 间ｈ（ｐ，ｑ，）（０＜ｐ，ｑ＜　）是自共轭的．