No abstract

No abstract

In this paper, the weak Orlicz space wL Φ is introduced and its applications to the martingale theory are discussed. In particular, a series of martingale inequalities including the maximal function inequality in weak Orlicz spaces are established; the relationships between these spaces are investigated. Moreover, the boundedness of several sublinear operators from one weak Orlicz space to another is proved; their vector-valued analogues are also considered. Keywordsweak Orlicz space, maximal function, martingale space, martingale inequality MSC(2000): 60G42, 60G46 Citation: Liu P D, Hou Y L, Wang M F. Weak Orlicz space and its applications to the martingale theory. Sci China Math, 2010, 53(4): 905-916,

No abstract

Abstract. In this paper we obtain some noncommutative multiplier theorems and maximal inequalities on semigroups. As applications, we obtain the corresponding individual ergodic theorems. Our main results extend some classical results of Stein and Cowling on one hand, and simplify the main arguments of Junge-Le Merdy-Xu's related work [15].

In this paper, we study the composition operator C Φ with a smooth but not necessarily holomorphic symbol Φ. A necessary and sufficient condition on Φ for C Φ to be bounded on holomorphic (respectively harmonic) weighted Bergman spaces of the unit ball in C n (respectively R n ) is given. The condition is a real version of Wogen's condition for the holomorphic spaces, and a non-vanishing boundary Jacobian condition for the harmonic spaces. We also show certain jump phenomena on the weights for the target spaces for both the holomorphic and harmonic spaces.

Y-shaped carbon nanofibers as a multi-branched carbon nanostructure have potential applications in electronic devices. In this article, we report that several types of Y-shaped carbon nanofibers are obtained from ethanol flames. These Y-shaped carbon nanofibers have different morphologies. According to our experimental results, the growth mechanism of Y-shaped carbon nanofibers has been discussed and a possible growth model of Y-shaped carbon nanofibers has been proposed.

In this paper, we investigate analytic symbols [Formula: see text] and [Formula: see text] when the weighted composition operator [Formula: see text] is complex symmetric on general function space [Formula: see text]. As applications, we characterize completely the compactness, normality and isometry of complex symmetric weighted composition operators. Especially, we show that the equivalence of compactness and Hilbert–Schmidtness, and the existence of non-normal complex symmetric operators for such operators, which answers one open problem raised by Noor in [On an example of a complex symmetric composition operators on [Formula: see text], J. Funct. Anal. 269 (2015) 1899–1901] for higher dimensional case.