Related papers: Dorronsoro's theorem and a small generalization

A proof is given of Rosenthal's \(\ell_1\) theorem.

We give a very simple proof of a strengthened version of Chernoff's Inequality. We derive the same conclusion from much weaker assumptions.

We extend the Caffarelli-Cordoba estimates to the vector case in two ways, one of which has no scalar counterpart, and we give a few applications for minimal solutions.

In this paper we show an index theorem for gerbes

We propose a simple proof of the vertical half-space theorem for Heisenberg space.

We investigate the interplay between invariant varieties of vector fields and the inflection locus of linear systems with respect to the vector field. Among the consequences of such investigation we obtain a computational criteria for the…

The purpose of this paper is to present a generalization of Forelli's theorem. In particular, we prove an all dimensional version of the two-dimensional theorem of Chirka of 2005.

We extend the Poincare'-Lyapounov-Nekhoroshev theorem from torus actions and invariant tori to general (non-abelian) involutory systems of vector fields and general invariant manifolds.

An approach is shown that proves various theorems of plane geometry in an algorithmic manner. The approach affords transparent proofs of a generalization of the Theorem of Morley and other well known results by casting them in terms of…

A very simple but useful almost sure convergence theorem of probability is given.

This work establishes a strong uniqueness property for a class of planar locally integrable vector fields. A result on pointwise convergence to the boundary value is also proved for bounded solutions.

In this paper, vector ultrametric spaces are introduced and a fixed point theorem is given for correspondences. Our main result generalizes a known theorem in ordinary ultrametric spaces.

In this article, we study the generalized Poincare problem from the opposite perspective, by establishing lower bounds on the degree of the vector field in terms of invariants of the variety.

I present a simple, elementary proof of Morley's theorem, highlighting the naturalness of this theorem.

Tensor fields depending on other tensor fields are considered. The concept of extended tensor fields is introduced and the theory of differentiation for such fields is developed.

Based on a generalization of Bohr's equivalence relation for general Dirichlet series, in this paper we study the sets of values taken by certain classes of equivalent almost periodic functions in their strips of almost periodicity. In…

We give an argument that magnetic monopoles should not exist. It is based on the concept of the index of a vector field. The thrust of the argument is that indices of vector fields are invariants of space-time orientation and of coordinate…

The Rado-Horn theorem provides necessary and sufficient conditions for when a collection of vectors can be partitioned into a fixed number of linearly independent sets. Such partitions exist if and only if every subset of the vectors…

We prove a version of the fundamental theorems of Morse Theory in the setting of finite spaces or partially ordered sets. By using these results we extend Forman's discrete Morse theory to more general cell complexes and derive the…

The motivation of this paper is to construct the theory of vector calculus of multivariate arithmetical functions. We prove analogues of integral theorems and Poincare's lemma.