## Endpoint estimates for the commutator of pseudo-differential operators

Published in Acta Mathematica Scientia

It is well known that the commutator Tb of the Calderón-Zygmund singular integral operator is bounded on Lp(Rn) for 1

Published in Acta Mathematica Scientia

It is well known that the commutator Tb of the Calderón-Zygmund singular integral operator is bounded on Lp(Rn) for 1

Published in Acta Mathematica Scientia

In this article, we introduce the concept of lacunary statistical convergence of order α of real number sequences and give some inclusion relations between the sets of lacunary statistical convergence of order α and strong Nθα(p)-summability. Furthermore, some relations between the spaces NθαSθα are examined.

Published in Acta Mathematica Scientia

The class f of almost convergent sequences was introduced by G.G. Lorentz, using the idea of the Banach limits [A contribution to the theory of divergent sequences, Acta Math. 80(1948), 167–190]. Let f0() and f() be the domain of the double sequential band matrix () in the sequence spaces f0 and f. In this article, the β. and γ-duals of the space f...

Published in Acta Mathematica Scientia

This article aims at studying two-direction refinable functions and two-direction wavelets in the setting ℝs, s > 1. We give a sufficient condition for a two-direction refinable function belonging to L2(ℝs). Then, two theorems are given for constructing biorthogonal (orthogonal) two-direction refinable functions in L2(ℝs) and their biorthogonal (or...

Published in Acta Mathematica Scientia

3-Lie algebras have close relationships with many important fields in mathematics and mathematical physics. This article concerns 3-Lie algebras. The concepts of 3-Lie coalgebras and 3-Lie bialgebras are given. The structures of such categories of algebras and the relationships with 3-Lie algebras are studied. And the classification of 4-dimensiona...

Published in Acta Mathematica Scientia

In this article, we prove a decomposition theorem for I2-convergent double sequences and introduce the notions of I2-Cauchy and I*2)-Cauchy double sequence, and then study their certain properties. Finally, we introduce the notions of regularly (I2,I)-convergence and (I2,I)-Cauchy double sequence.

Published in Acta Mathematica Scientia

Recently, Suzuki [T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc. Amer. Math. Soc. 136 (2008), 1861-1869] proved a fixed point theorem that is a generalization of the Banach contraction principle and characterizes the metric completeness. Paesano and Vetro [D. Paesano and P. Vetro, Suzuki's type c...

Published in Acta Mathematica Scientia

The object of this article is to investigate inclusion, radius, and other various properties of subclasses of multivalent analytic functions, which are defined by using an extended version of the Owa-Srivastava fractional differintegral operator Ω(λ, p).

Published in Acta Mathematica Scientia

Let (M, T) be a smooth closed manifold with a smooth involution T whose fixed point set is a disjoint union of an even-dimensional real projective space and a Dold manifold. In some cases, the equivariant bordism classes of (M, T) are determined.

Published in Acta Mathematica Scientia

The traditional model selection criterions try to make a balance between fitted error and model complexity. Assumptions on the distribution of the response or the noise, which may be misspecified, should be made before using the traditional ones. In this article, we give a new model selection criterion, based on the assumption that noise term in th...