Erratum to: Singular Adams inequality for biharmonic operator on Heisenberg Group and its applications

Weak Type Estimates for a Singular Convolution Operator on the Heisenberg Group

On the Heisenberg group Hn with coordinates (z, t) ∈ Cn × R, define the distribution K(z, t) = L(z)δ(t), where L(z) is a homogeneous distribution on Cn of degree −2n, smooth away from the origin and δ(t) is the Dirac mass in the t variable. We prove that the operator given by convolution with K maps H1(Hn) to weak L1(Hn).

Singular Convolution Operators on the Heisenberg Group

1. Statement of results and outline of method. The purpose of this note is to announce results dealing with convolution operators on the Heisenberg group. As opposed to the well-known situation where the kernels are homogeneous and C°° away from the origin, the kernels we study are homogeneous but have singularities on a hyperplane. Convolution operators with such kernels arise in the study of ...

Meda Inequality for Rearrangements of the Convolution on the Heisenberg Group and Some Applications

The Meda inequality for rearrangements of the convolution operator on the Heisenberg group Hn is proved. By using the Meda inequality, an O’Neil-type inequality for the convolution is obtained. As applications of these results, some sufficient and necessary conditions for the boundedness of the fractional maximal operator MΩ,α and fractional integral operator IΩ,α with rough kernels in the spac...

Picone’s Identity for the P-biharmonic Operator with Applications

In this article, a Picone-type identity for the weighted p-biharmonic operator is established and comparison results for a class of half-linear partial differential equations of fourth order based on this identity are derived.

Subelliptic equations with singular nonlinearities on the Heisenberg group