Wavelets and Real Interpolation of Besov Spaces

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.

Some Notes of Homogeneous Besov–Lorentz Spaces

“…If p 0 ≠ p 1 , generally speaking, ( _ B s,q p 0 , _ B s,q p 1 ) θ,r will fall outside of the scale of Besov spaces. Tere are many works which considered the real interpolation, see [1][2][3][4][5][6][7][8][9][10][11][12]. But does ( _ B s,q p 0 , _ B s,q p 1 ) θ,r be the Besov-Lorentz space _ B s,q p,r which is given in [1]?…”