We analyze the rate of convergence towards self-similarity for the subcritical KellerSegel system in the radially symmetric two-dimensional case and in the corresponding one-dimensional case for logarithmic interaction. We measure convergence in Wasserstein distance. The rate of convergence towards self-similarity does not degenerate as we approach the critical case. As a byproduct, we obtain a...

We analyze the rate of convergence towards self-similarity for the subcritical KellerSegel system in the radially symmetric two-dimensional case and in the corresponding one-dimensional case for logarithmic interaction. We measure convergence in Wasserstein distance. The rate of convergence towards self-similarity does not degenerate as we approach the critical case. As a byproduct, we obtain a...

see for instance [29]. Notice that the exponent p or q could be larger than N+2 N−2 . Hence the usual Sobolev space H 0 (Ω)×H1 0 (Ω) is not suitable to handle the problem. To study the problem (1.2) under the condition (1.3), a key observation was done by Hulshof and Van de Vorst [16], De Figueiredo and Felmer [9]. In order to solve this problem, the main idea is to destroy the symmetry between...

We obtain Fourier inequalities in the weighted Lp spaces for any 1<p<∞ involving Hardy–Cesàro and Hardy–Bellman operators. extend these results to product Hardy p⩽1. Moreover, boundedness of Hardy-Cesàro Hardy-Bellman operators various (Lebesgue, Hardy, BMO) is discussed. One our main tools an appropriate version Hardy–Littlewood–Paley inequality ‖fˆ‖Lp′,q≲‖f‖Lp,q.

Sik,?It was with great interest that I read in J01'1 issue Colonel Wimberley's article on the out iea Dengue-like fever amongst the 15tli Sikhs, It struck me that if there is a differential diagnosis a < between ' Breakbone Dengue ' and the Seven-Day I e\ei c cribed by Major Leonard Rogers?then these interesting cases must fall under the latter heading?and this, in spi e the fact that the fever...

Using recent characterizations of the compactness of composition operators on HardyOrlicz and Bergman-Orlicz spaces on the ball ([2, 3]), we first show that a composition operator which is compact on every Hardy-Orlicz (or Bergman-Orlicz) space has to be compact on H∞. Then, although it is well-known that a map whose range is contained in some nice Korányi approach region induces a compact comp...