We study interpolating sequences in the unit disk for the intersection of the Bloch space B with the Hardy space H^p , 01 , we show that the interpolating Blaschke sequences for B∩ H^p coincide with those of B, that is, the H^p condition restricts the interpolation data but imposes no additional geometric separation or density requirements. For every 0
In this paper, we investigate the boundedness and compactness of the inclusion mapping id:Flog(p,p-2,s)-> Tlog,p,s infinity(mu) . As an application, we establish complete characterizations for the boundedness, compactness, and operator norm of the Volterra integral operators Jg and Ig acting on Flog(p,p-2,s) .
In this paper, we study two constrained cases of the Kadomtsev-Petviashvili hierarchy, named the generalized constrained Kadomtsev-Petviashvili and the generalized constrained modified Kadomtsev-Petviashvili hierarchies. The additional symmetries and gauge transformations for the generalized constrained Kadomtsev-Petviashvili hierarchy are given. These flows form a subalgebra of the Virasoro algebra. We give explicit formulas for the action of the additional flows for the generalized constrained Kadomtsev-Petviashvili and the generalized constrained modified Kadomtsev-Petviashvili hierarchies on tau functions. The additional flows for the generalized constrained Kadomtsev-Petviashvili hierarchy commuted with gauge transformations preserve their original form, up to shifting of the additional flows by the sum of two squared eigenfunction symmetry flows.
We consider weighted Funk transforms on the unit 2-sphere S^2 where the weights are given as finite Fourier series in the angle variable. We study the injectivity of the transform depending on the weight. Using the consistency method suggested by the author of this article, we obtain an injectivity condition for different classes of functions. The approach can give an inversion formula for some weights. Such inversions have theoretical significance in convexity theory, integral geometry, spherical tomography, and others.
