Browsing by Subject "BOUNDEDNESS"

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  • Martikainen, Henri; Mourgoglou, Mihalis; Vuorinen, Emil (2021)
    We develop a new general method to prove various non-doubling local Tb theorems. The method combines the non-homogeneous good lambda method of Tolsa, the big pieces Tb theorem of Nazarov-Treil-Volberg and a new change of measure argument based on stopping time techniques. We also improve known results and discuss some further applications.
  • Hurri-Syrjänen, Ritva; Ohno, Takao; Shimomura, Tetsu (2021)
    We give Trudinger-type inequalities for Riesz potentials of functions in Orlicz-Morrey spaces of an integral formover non-doublingmetricmeasure spaces. Our results are new even for the doubling metric measure setting. In particular, our results improve and extend the previous results in Morrey spaces of an integral form in the Euclidean case.
  • Airta, Emil; Vuorinen, Emil; Martikainen, Henri (2022)
    We develop product space theory of singular integrals with mild kernel regularity. We study these kernel regularity questions specifically in situations that are very tied to the T1 type arguments and the corresponding structural theory. In addition, our results are multilinear.
  • Cai, Yuhua; Geritz, Stefanus (2020)
    We study resident-invader dynamics in fluctuating environments when the invader and the resident have close but distinct strategies. First we focus on a class of continuous-time models of unstructured populations of multi-dimensional strategies, which incorporates environmental feedback and environmental stochasticity. Then we generalize our results to a class of structured population models. We classify the generic population dynamical outcomes of an invasion event when the resident population in a given environment is non-growing on the long-run and stochastically persistent. Our approach is based on the series expansion of a model with respect to the small strategy difference, and on the analysis of a stochastic fast-slow system induced by time-scale separation. Theoretical and numerical analyses show that the total size of the resident and invader population varies stochastically and dramatically in time, while the relative size of the invader population changes slowly and asymptotically in time. Thereby the classification is based on the asymptotic behavior of the relative population size, and which is shown to be fully determined by invasion criteria (i.e., without having to study the full generic dynamical system). Our results extend and generalize previous results for a stable resident equilibrium (particularly, Geritz in J Math Biol 50(1):67-82, 2005; Dercole and Geritz in J Theor Biol 394:231-254, 2016) to non-equilibrium resident population dynamics as well as resident dynamics with stochastic (or deterministic) drivers.