By Hans Triebel

This publication is the continuation of neighborhood functionality areas, warmth and Navier-Stokes Equations (EMS Tracts in arithmetic, quantity 20, 2013) by way of the writer. a brand new process is gifted to express family members among Sobolev areas, Besov areas, and Hölder-Zygmund areas at the one hand and Morrey-Campanato areas at the different. Morrey-Campanato areas expand the thought of features of bounded suggest oscillation. those areas play a vital position within the thought of linear and nonlinear PDEs. bankruptcy 1 (Introduction) describes the most motivations and intentions of this e-book. bankruptcy 2 is a self-contained creation to Morrey areas. bankruptcy three bargains with hybrid smoothness areas (which are among neighborhood and international areas) in Euclidean n-space in response to the Morrey-Campanato refinement of the Lebesgue areas. The awarded strategy, which depends upon wavelet decompositions, is utilized in bankruptcy four to linear and nonlinear warmth equations in worldwide and hybrid areas. The bought assertions approximately functionality areas and nonlinear warmth equations are utilized in Chapters five and six to check Navier-Stokes equations in hybrid and international areas. This e-book is addressed to graduate scholars and mathematicians who've a operating wisdom of simple components of (global) functionality areas and who're attracted to functions to nonlinear PDEs with warmth and Navier-Stokes equations as prototypes. A book of the eu Mathematical Society (EMS). dispensed in the Americas by means of the yankee Mathematical Society.