2026/07/30 by Bingyang Hu, Shuaibing Luo, Jie Xiao +1
Mathematics · #math.CV #math.FA
arxiv created 2026/07/30 · arxiv updated 2026/07/31
In this paper, we obtain non-testing characterizations, in terms of dyadic capacity gauges, of the boundedness and compactness of the differentiation operator (d)/(dz):QK\longrightarrow Lq(W dA), 0<q<∞. We also characterize the limiting case as q→0+, formulated in terms of a logarithmic geometric mean, while the endpoint q=∞ is treated separately using a standard testing argument. These results greatly extend the previous work on \mathcal Qp-spaces to the general setting of QK-spaces. As applications, we characterize composition operators and Volterra-type integral operators between different QK-spaces. In particular, the off-diagonal characterization established here, together with the previously established diagonal case, completely resolves Zhao's 2009 open question on composition operators between \mathcal Qp-spaces.