We define a class of paraproducts on Heisenberg type groups. We prove they have L2 boundedness. We also study Calderón-Zygmund operators, and prove they are bounded operators which map Lp to Lp, L1 to L1,∞ and H1 to L1. Then we prove the paraproducts are also Calderón-Zygmund operators and they also satisfy two important properties that Pb1=b and Pbt(1)=0 in the sense of distribution.
Let H be an infinite-dimensional separable complex Hilbert space and B(H) be the algebra of all bounded linear operators on H. An operator T∈B(H) is said to have the single-valued extension property, if for every open set U⊆C, the only analytic solution f:U→H of the equation (T-λI)f(λ)=0 for all λ∈U is zero function on U; T∈B(H) is said to have the stability of the single-valued extension property if T+K has the single-valued extension property for any compact operator K∈B(H). In this paper, we characterize 2×2 upper triangular operator matrices for which the single valued extension property is stable under compact perturbations.
Let U=Tri(A, M, B) be the triangular algebra with identity I, and let φ={φn}n∈N be a family of linear maps on U. We show that if φ={φn}n∈N satisfying φn(UV+VU)=∑i+j=n(φi(U)φj(V)+φi(V)φj(U)) whenever U, V∈U with UV=VU=I, then it is a higher derivation. As its application, we give a different characterization of Jordan higher derivations on nest algebras.
We study the approximation of the inverse shearlet transform using discrete series. We first introduce the infinite series and finite series defined by the inverse shearlet transforms. We then investigate the shearlet generator space by introduced by Kittipoom et al., some important properties are given. For the shearlet generator space, we show that the infinite series tend to the function to be reconstructed in L2-norm as the sampling density tends to infinity. For the admissible shearlet space, we show that the finite series also tend to the function to be reconstructed in L2-norm as the sampling density tends to infinity.
For 1 < r < ∞ and Banach space B=Lr(Ω, F, μ), we study the Hardy-Lorentz space Hp,q(Rn, B) of B-value tempered distribution on Euclidean space Rn and the interpolation between the Hardy-Lorentz spaces, where 0 < p < ∞ and 0 < q ≤ ∞. We obtain a sequence of equivalent characterization and an atomic decomposition of Hp,q(Rn, B). If Ω={1}, then Hp,q(Rn, B)=Hp,q(Rn) is the classical case; if Ω=Z is the set of all integers, μ is the counting measure on Z and r=2, 0 < p < ∞, q=∞, then Hp,q(Rn, B)=Hp,∞(Rn, l2) is the case of Grafakos and He [Weak Hardy spaces, Preprint, 2014].
In this paper, based on the minimal projective bimodule resolution of a cluster-tilted algebra given by Furuya, we define the so-called "comultiplication" structure of the minimal projective bimodule resolution, and show that the cup product of Hochschild cohomology ring of the cluster-tilted algebra is essentially juxtaposition of parallel paths up to sign. As a consequence, we determine the structure of the Hochschild cohomology ring under the cup product by giving an explicit presentation via generators and relations.
In this paper, we study the representation problems of the conjugate spaces of some l0 class F-normed spaces, obtain the algebra representation continued equality (l0)*(c0)*(c00)*(c000)*c00, and the topological representation theorem ((c000)*,sw*)=c000.
We solve a problem of Terence Tao. We prove that for any K≥2 and sufficiently large N, the number of primes p between N and (1+1/K)N such that |kp+jai+l| is composite for all 1≤a, |j|, k≤K, 1 ≤ i ≤ K log N and l in any set LN⊆{-KN, …, KN} of cardinality K with jai+l≠0 is at least CK M/log N, where CK>0 depending only on K.
Firstly, we give a combinatorial bijection between the self-inverse n-color compositions of 2ν the n-color compositions of ν+1 along with the n-color compositions of ν-1 in this paper, and we also obtain a combinatorial identity by using some related enumeration formulas. Then, we give a relationship about the number of the self-inverse n-color compositions of positive integer, the Fibonacci number and the Lucas number. In addition, a combinatorial bijection between the self-inverse n-color compositions of odd and the self-inverse n-color compositions of even is presented. Finally, we get some identities about the number of the self-inverse n-color compositions of positive integer and the number of the others compositions with constraint conditions.
Under some suitable conditions, we introduce a new modified Ishikawa iterative algorithm with errors for converging strongly to a common element of the set of common fixed points of infinite family of nonexpansive mappings in a reflexive Banach space. The results presented here improve and generalize some known results and an example is given to demonstrate the application of our main results.
The author establishes the Lp boundedness of two classes of maximal operators related to rough singular integrals supported by compound subvarieties. Our main results greatly improve and generalize some known results. As applications, several Lp estimates of singular integrals, Marcinkiewicz integrals and maximal operators related to Marcinkiewicz integrals are also obtained.