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A framework for discrete bilinear spherical averages and applications to -improving estimates
Theresa C. Anderson, Angel V. Kumchev, Eyvindur A. Palsson
We decompose the discrete bilinear spherical averaging operator into simpler operators in several ways. This leads to a wide array of extensions, such as to the simplex averaging o…
A structure theorem on doubling measures with different bases
Theresa C. Anderson, Bingyang Hu
In this paper, we prove a structure theorem for the infinite union of -adic doubling measures via techniques which involve far numbers. Our approach extends the results of Wu in…
Sharp Mei's lemma with different bases
Theresa C. Anderson, Bingyang Hu
In this paper, we prove a sharp Mei's Lemma with assuming the bases of the underlying general dyadic grids are different. As a byproduct, we specify all the possible cases of adjac…
On the general dyadic grids in
Theresa C. Anderson, Bingyang Hu
Adjacent dyadic systems are pivotal in analysis and related fields to study continuous objects via collections of dyadic ones. In our prior work (joint with Jiang, Olson and Wei) w…
Bounds for discrete multilinear spherical maximal functions in higher dimensions
Theresa C. Anderson, Eyvindur Ari Palsson
We find the sharp range for boundedness of the discrete bilinear spherical maximal function for dimensions . That is, we show that this operator is bounded on $l^{p}(\mat…
Bounds for discrete multilinear spherical maximal functions
Theresa C. Anderson, Eyvindur Ari Palsson
We define a discrete version of the bilinear spherical maximal function, and show bilinear bounds for $d \ge…