D. Adams and &. J. Xiao, Morrey spaces in harmonic analysis, Arkiv f??r Matematik, vol.50, issue.2, pp.201-230, 2012.
DOI : 10.1007/s11512-010-0134-0

L. Caffarelli and &. A. Vasseur, Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation, Annals of Mathematics, vol.171, issue.3, 1903.
DOI : 10.4007/annals.2010.171.1903

D. Chamorro, A molecular method applied to a non-local PDE in stratified Lie groups, Journal of Mathematical Analysis and Applications, vol.413, issue.2, pp.583-608, 2014.
DOI : 10.1016/j.jmaa.2013.12.006

URL : https://hal.archives-ouvertes.fr/hal-00840246

D. Chamorro and &. P. Lemarié-rieusset, Quasi-geostrophic equations, nonlinear Bernstein inequalities and $\alpha$-stable processes, Revista Matem??tica Iberoamericana, vol.28, issue.4, pp.1109-1122, 2012.
DOI : 10.4171/RMI/705

R. Coifmann and &. G. Weiss, Extensions of Hardy spaces and their use in analysis, Bull Amer, Math. Soc, vol.83, issue.4, 1977.

P. Constantin and &. J. Wu, Behavior of Solutions of 2D Quasi-Geostrophic Equations, SIAM Journal on Mathematical Analysis, vol.30, issue.5, pp.937-948, 1999.
DOI : 10.1137/S0036141098337333

P. Constantin and &. J. Wu, Regularity of Hölder continuous solutions of the supercritical quasi-geostrophic equation, Annales de l'Institut Henri Poincaré. Analyse non linéaire, pp.1103-1110, 2008.

A. Cordoba and &. D. Cordoba, A Maximum Principle Applied to Quasi-Geostrophic Equations, Communications in Mathematical Physics, vol.46, issue.3, pp.511-528, 2004.
DOI : 10.1007/s00220-004-1055-1

E. , D. Nezza, G. Palatucci, and &. E. Valdinoci, Hitchhiker's guide to the fractional Sobolev spaces, Bulletin des Sciences Mathématiques, vol.136, pp.521-573, 2012.

D. Goldberg, A local version of real Hardy spaces, Duke Mathematical Journal, vol.46, issue.1, p.1, 1979.
DOI : 10.1215/S0012-7094-79-04603-9

L. Grafakos, Classical and Modern Fourier Analysis, 2004.

N. Jacob, Pseudo-Differential Operators and Markov Processes, 2001.

N. Jacob, Pseudo-Differential Operators and Markov Processes, 2002.

G. Karch, Nonlinear evolution equations with anomalous diffusion, Lecture Notes, 2010.

A. Kiselev and &. F. Nazarov, Variation on a theme of caffarelli and vasseur, Journal of Mathematical Sciences, vol.167, issue.1, pp.58-72, 2009.
DOI : 10.1007/s10958-010-9842-z

P. G. Lemarié and ?. Rieusset, Recent developments in the Navier?Stokes problem, 2002.

F. Marchand, Propagation of Sobolev regularity for the critical dissipative quasi-geostrophic equation, Asymptotic Analysis, vol.49, pp.3-4, 2006.

J. Peetre, On the theory of Lp,?? spaces, Journal of Functional Analysis, vol.4, issue.1, pp.71-87, 1969.
DOI : 10.1016/0022-1236(69)90022-6

K. Sato, Lévy Processes and Infinitely Divisible Distributions, Cambridge studies in advanced mathematics, 1999.

L. Silvestre, V. Vicol, and &. , On the Loss of Continuity for Super-Critical Drift-Diffusion Equations, Archive for Rational Mechanics and Analysis, vol.226, issue.3, pp.845-877, 2013.
DOI : 10.1007/s00205-012-0579-3

E. M. Stein, Singular Integrals and Differentiability Properties of Functions, 1970.

E. M. Stein, Harmonic Analysis, 1993.

D. W. Stroock, An Introduction to the Theory of Large Deviations, 1984.
DOI : 10.1007/978-1-4613-8514-1

A. Torchinski, Real-Variable methods in Harmonic Analysis, 2004.

N. Th and . Varopoulos, Hardy-Littlewood theory for semigroups, J. Funct. Anal, vol.63, pp.240-260, 1985.

C. Zorko, Morrey space, Proc. Amer, pp.586-592, 1986.
DOI : 10.1090/S0002-9939-1986-0861756-X