doi:10.1155/2019/4763450engAbadias, L.Miana, P.J.Quasigeostrophic Equations for Fractional Powers of Infinitesimal GeneratorsART-2019-111273In this paper we treat the following partial differential equation, the quasigeostrophic equation: d / dt + u · grad f = - s - A a f, 0 = a = 1, where (A, D (A)) is the infinitesimal generator of a convolution C 0 -semigroup of positive kernel on L p (R n), with 1 = p < 8. Firstly, we give remarkable pointwise and integral inequalities involving the fractional powers (- A) a for 0 = a = 1. We use these estimates to obtain L p -decayment of solutions of the above quasigeostrophic equation. These results extend the case of fractional derivatives (taking A = ¿, the Laplacian), which has been studied in the literature.2019http://zaguan.unizar.es/record/7893510.1155/2019/4763450http://zaguan.unizar.es/record/78935oai:zaguan.unizar.es:78935info:eu-repo/grantAgreement/ES/DGA/E26-17Rinfo:eu-repo/grantAgreement/ES/MINECO/MTM2016-77710-PJournal of Function Spaces 2019, 4763450 (2019), [7 pp]byhttp://creativecommons.org/licenses/by/3.0/es/info:eu-repo/semantics/openAccess