Cholewa, Jan W.Rodríguez Bernal, Aníbal2023-11-162023-11-162022Cholewa, J. W., & Rodriguez-Bernal, A. (2020). Sharp estimates for homogeneous semigroups in homogeneous spaces. Applications to PDEs and fractional diffusion in ℝN. Communications In Contemporary Mathematics, 24(01). https://doi.org/10.1142/s02191997205007040219-199710.1142/S0219199720500704https://hdl.handle.net/20.500.14352/88740In this paper, we analyze evolution problems associated to homogenous operators. We show that they have an homogenous associated semigroup of solutions that must satisfy some sharp estimates when acting on homogenous spaces and on the associated fractional power spaces. These sharp estimates are determined by the homogeneity alone. We also consider fractional diffusion problems and Schr ̈odinger type problems as well. We apply these general results to broad classes of PDE problems including heat or higher order parabolic problems and the associated fractional and Schr ̈odinger problems or Stokes equations. These equations are considered in Lebesgue or Morrey spaces.engjournal articlehttps://doi.org/10.1142/S0219199720500704https://www.worldscientific.com/doi/abs/10.1142/S0219199720500704restricted access517.98Homogeneous spacesLinear parabolic equationsFractional diffusion equationsStokes equationsSemigroups of linear operatorsSchrödinger equationsAnálisis funcional y teoría de operadores1202 Análisis y Análisis Funcional