ISSN 1439-8516 CN 11-2039/O1
In this paper, we characterize the sharp boundedness of the one-sided fractional maximal function for one-weight and two-weight inequalities. Also a new two-weight testing condition for the one-sided fractional maximal function is introduced extending the work of Martín-Reyes and de la Torre. Improving some extrapolation result for the one-sided case, we get weak sharp bounded estimates for one-sided fractional maximal function and weak and strong sharp bounded estimates for one-sided fractional integral.
-εNΔNu+V(x)|u|N-2u=Q(x)f(u) in RN,
0<u∈W1,N(RN),u(x)
0,In this paper, the authors establish the boundedness of commutators generated by strongly singular Calderón-Zygmund operators and weighted BMO functions on weighted Herz-type Hardy spaces. Moreover, the corresponding results for commutators generated by strongly singular Calderón-Zygmund operators and weighted Lipschitz functions can also be obtained.
Let X denote a compact metric space with distance d and F:X×R→X or Ft:X→X denote a C0-flow. From the point of view of ergodic theory, all important dynamical behaviors take place on a full measure set. The aim of this paper is to introduce the notion of Banach upper density recurrent points and to show that the closure of the set of all Banach upper density recurrent points equals the measure center or the minimal center of attraction for a C0-flow. Moreover, we give an example to show that the set of quasi-weakly almost periodic points can be included properly in the set of Banach upper density recurrent points, and point out that the set of Banach upper density recurrent points can be included properly in the set of recurrent points.
By using the stable t-structure induced by an adjoint pair, we extend several results concerning recollements to upper (resp. lower) recollements. These include the fundamental results of Parshall and Scott on comparisons of recollements, Wiedemann's result on the global dimension and Happel's result on the finitistic dimension, occurring in a recollement (Db(A'),Db(A),Db(A″)) of bounded derived categories of Artin algebras. We introduce and describe a triangle expansion of a triangulated category and illustrate it by examples.
A graph is 1-planar if it can be drawn on the plane so that each edge is crossed by at most one other edge. In this paper, we prove that every 1-planar graph G with maximum degree Δ(G) ≥ 12 and girth at least five is totally (Δ(G)+1)-colorable.
Continuing our previous work (arXiv:1509.07981v1), we derive another global gradient estimate for positive functions, particularly for positive solutions to the heat equation on finite or locally finite graphs. In general, the gradient estimate in the present paper is independent of our previous one. As applications, it can be used to get an upper bound and a lower bound of the heat kernel on locally finite graphs. These global gradient estimates can be compared with the Li-Yau inequality on graphs contributed by Bauer et al.[J. Differential Geom., 99, 359-409(2015)]. In many topics, such as eigenvalue estimate and heat kernel estimate (not including the Liouville type theorems), replacing the Li-Yau inequality by the global gradient estimate, we can get similar results.
Our contribution in this paper is to propose an iterative algorithm which does not require prior knowledge of operator norm and prove strong convergence theorem for approximating a solution of split common fixed point problem of demicontractive mappings in a real Hilbert space. So many authors have used algorithms involving the operator norm for solving split common fixed point problem, but as widely known the computation of these algorithms may be difficult and for this reason, authors have recently started constructing iterative algorithms with a way of selecting the step-sizes such that the implementation of the algorithm does not require the calculation or estimation of the operator norm. We introduce a new algorithm for solving the split common fixed point problem for demicontractive mappings with a way of selecting the step-sizes such that the implementation of the algorithm does not require the calculation or estimation of the operator norm and then prove strong convergence of the sequence in real Hilbert spaces. Finally, we give some applications of our result and numerical example at the end of the paper.
Let C be a triangulated category with a proper class ε of triangles. We prove that there exists an Avramov-Martsinkovsky type exact sequence in C, which connects ε-cohomology, ε-Tate cohomology and ε-Gorenstein cohomology.
Let A be an expansive dilation on Rn and φ:Rn×[0, ∞)→[0, ∞) an anisotropic Musielak-Orlicz function. Let HAφ(Rn) be the anisotropic Hardy space of Musielak-Orlicz type defined via the grand maximal function. In this article, the authors establish its molecular characterization via the atomic characterization of HAφ(Rn). The molecules introduced in this article have the vanishing moments up to order s and the range of s in the isotropic case (namely, A:=2In×n) coincides with the range of well-known classical molecules and, moreover, even for the isotropic Hardy space Hp(Rn) with p∈(0, 1] (in this case, A:=2In×n, φ(x, t):=tp for all x∈Rn and t∈[0, ∞)), this molecular characterization is also new. As an application, the authors obtain the boundedness of anisotropic Calderón-Zygmund operators from HAφ(Rn) to Lφ(Rn) or from HAφ(Rn) to itself.
