Homogeneous Besov Spaces on Stratified Lie Groups and Their Wavelet Characterization
Homogeneous Besov Spaces on Stratified Lie Groups and Their Wavelet Characterization
We establish wavelet characterizations of homogeneous Besov spaces on stratified Lie groups, both in terms of continuous and discrete wavelet systems. We first introduce a notion of homogeneous Besov space<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mover accent="true"><mml:mi>B</mml:mi><mml:mo>˙</mml:mo></mml:mover><mml:mrow><mml:mi>p</mml:mi><mml:mo>,</mml:mo><mml:mi>q</mml:mi></mml:mrow><mml:mi>s</mml:mi></mml:msubsup></mml:math>in terms of a Littlewood-Paley-type decomposition, in analogy to the well-known characterization of the Euclidean case. Such decompositions can …