Boundedness of some sublinear operators in weighted Herz-type spaces

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Boundedness of sublinear operators on Herz spaces with variable exponent and application to wavelet characterization (2010, methodology): “As an application of [ 15 ], noting that the Hardy–Littlewood maximal operator M is a sublinear operator satisfying the assumption above, Nakai, Tomita and Yabuta [18] have proved the density of the set of all infinitely differentiable functions with compact support in weighted Herz spaces.”
The Navier-Stokes equations and weak Herz spaces (2011, methodology): “The theories of the Herz space and the Herz-type Hardy space were developed by, for example, [10], [11], [34], [35], [36], [37], [41] etc.”