This paper deals with an extension of Hardy--Hilbert's inequality with a best constant factor by using the method of weight coefficient, and also considers its particular results.
. If, for every f ∈F, f(z)≠ a(z) and f(z)≠ b(z), then F is normal in D. This improves the classic Montel's normality criterion. Moreover, we discuss the normality of families of meromorphic functions in which every function shares two holomorphic functions with its derivative.
In this paper, it is shown that two admissible meromorphic functions in the unit disc must be identical, provided that they share five small functions CM or five values IM in one angular domain.
satisfys N≤Z(G). In this article, we classify completely the groups central extention of H by N gets, when |N|=p and H is an inner abelian p-group.
-primary w-ideal of R is a w-envelope of some power of the prime ideal . Moreover, we show some new equivalent characterizations of π-domains by utilizing w-operations and with the supplement of t- and v-operations.
has the properties P(k) and Q(k), where denotes the family of all infinite subsets of 
whose upper density is not less than s. Furthermore, we prove that for any positive integer k, S is an -scrambled set of (X,f) if and only if S is an -scrambled set of (X,fk), where s,t∈[0,1].
This paper proves that two regular homogeneous uniform Moran sets are quasi-Lipschitz equivalent if and only if they have the same Hausdorff dimension.
In this paper, by virtue of the geometric structure on the space of boundary conditions, we prove the equality between analytic and geometric multiplicities of a self-adjoint high-order ordinary differential operator, which is an analogue to the case of the regular Sturm--Liouville problem.
is a nonnegative function satisfying the reverse Hölder inequality. In this article, the author investigates some properties of the Riesz potential ILα=L-α/2 on the Campanato-type spaces ΛβL and the Hardy-type spaces HpL on Hn.
where constant 
. We may call the above expression T-A (Thonhauser and Albrecher) objective function. For the diffusion risk model with constant interest force, maximization of T-A objective function is solved by stochastic control theory (HJB equations): For bounded dividend intensity, optimal strategy is a threshold strategy; for unbounded dividend intensity, optimal strategy is a barrier strategy.
