Abstract
In view of the importance of Besov space in harmonic analysis, differential equations, and other fields, Jaak Peetre proposed to find a precise description of (Bp0s0,q0,Bp1s1,q1)θ,r. In this paper, we come to consider this problem by wavelets. We apply Meyer wavelets to characterize the real interpolation of homogeneous Besov spaces for the crucial index p and obtain a precise description of (B˙p0s,q,B˙p1s,q)θ,r.
Highlights
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Since the middle of 20th century, the study of interpolation space has greatly promoted the development of function space, operator theory, and developed a set of perfect mathematical theories
It greatly enriches the theory of harmonic analysis, see [1,2,3,4]
Summary
For the real interpolation of Besov spaces, we can refer to [9,10,11,12,13,14,15,16]. J. Peetre proposed to consider the real interpolation of Besov spaces in [4]. The wavelet characterization of real interpolation spaces of Besov spaces provides people with an effective means to study the continuity of linear operators and bilinear operators on such spaces. We are using this point to study the well-posedness of non-linear fluid equations.
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