  The Menchov-Rademacher inequality is an inequality in harmonic analysis that
bounds the $L_2$ norm of a certain maximal operator. It was first established
in order to prove almost everywhere convergence of a one-parameter series of
orthogonal functions. When two-parameter series of orthogonal functions is
considered, the exact way the series is grouped becomes essential. We will
consider grouping of a two-parameter series, generated by a sequence of right
triangles with a vertex at the origin, who might be non-equilateral, and prove
almost everywhere convergence when the eccentricity of those triangles is
bounded. In order to carry out the proof, we will derive an analogue of the
Menchov-Rademacher inequality for right triangles.

Classical Analysis and ODEs