We investigate the single link mixed loss-delay FIFO system with the exponential holding time distribution, the Markovian interarrival process for the narrow-band calls, and the general independently and identically distributed interarrival process for the wide-band calls. This is achieved by combining the embedded Markov chain method and the matrix-analytic technique.
The main result of this paper is some quantitative estimates for nonlinear commutators under the complex interpolation methods and more general interpolation scales with holomorphic structures. We also investigate the spectral behaviour of bounded linear operators under this kind of interpolation methods.
We establish the connection between the variants of Schechter's complex interpolation methods, Peetre-Gustavsson's interpolation methods, and the Calderon-Lozanovskii construction on vector-valued Banach lattices. As applications, we show that the uniform convexity and the UMD property are stable byinterpolation.
In this paper, we study the K-envelopes of the real interpolation methods with function space parameters in the sense of Brudnyi and Kruglyak [Y. A. Brudnyi and N. Ja. Kruglyak, Interpolation functors and interpolation spaces(North-Holland, Amsterdam, Netherlands, 1991)]. We estimate the upper bounds of the K-envelopes and the interpolation norms of bounded operators for the K Φ-methods in terms of the fundamental function of the rearrangement invariant space related to the function space parameter Φ. The results concerning the quasi-power parameters and the growth/continuity envelopes in function spaces are obtained.
This paper concerns some properties of Lions-Peetre's interpolation methods of constants and means associated with quasi-power functions, and their applications in harmonic analysis, martingale inequalities, and geometric properties of Banach spaces. We describe Besov-Orlicz spaces and Triebel-Lizorkin-Orlicz spaces in terms of interpolation and wavelet bases. We study the commutators of quasi-logarithmic operators and singular integral operators, Hankel operators in Schatten-Orlicz classes, martingale inequalities for the partial derivative-variation, and the stability of multi-dimensional uniform rotundity under interpolation.
Some quantitative estimates concerning multi-dimensional rotundity, weak noncompactness, and certain spectral inequalities are formulated for Lions-Schechter's complex methods of interpolation with derivatives.
We investigate some properties of Hilbert spaces and bounded linear operators under quadratic interpolation in both qualitative and quantitative ways. Interpolation type, reiteration, interpolation methods associated with quasi-power function parameters, nonlinear commutator estimates, and interpolation of certain operators and spectral properties are under consideration.
We formulate the quantitative version of interpolation theorems on compactness and weak compactness, the improved estimate for the k-uniform rotundity, and even the stability of the nearly uniform convexity under Lions-Peetre's interpolation methods of constants and means associated with quasi-power function parameters.