In this paper, we establish new generalizations and results in shift-invariant subspaces of mixed-norm Lebesgue spaces Lp→(Rd). We obtain a Hölder inequality, Minkowski convolution convolution-Hölder type inequality stability theorem to case the setting subspace Our unify refine existing literature.

This paper gives an essentially self-contained exposition (except for appeal to the Lojasiewicz gradient inequality) of geometric invariant theory from a differential viewpoint. Central ingredients are moment-weight inequality (relating Mumford numerical invariants norm moment map), negative flow map squared, and Kempf-Ness function.

In this work, we investigate the tensor inequalities in t-product formalism. The involving power are proved to hold similarly as standard matrix scenarios. We then focus on norm inequalities. well-known arithmetic-geometric mean inequality, Hölder and Minkowski inequality generalized tensors. Furthermore, obtain some t-eigenvalue

We prove a fractional version of Poincaré inequalities in the context of R endowed with a fairly general measure. Namely we prove a control of an L norm by a non local quantity, which plays the role of the gradient in the standard Poincaré inequality. The assumption on the measure is the fact that it satisfies the classical Poincaré inequality, so that our result is an improvement of the latter...