Lp Fourier multipliers on compact Lie groups

In this paper we prove Lp multiplier theorems for invariant and non-invariant operators on compact Lie groups in the spirit of the well-known Hormander-Mikhlin theorem on Rn and its variants on tori Tn. We also give applications to a-priori estimates for non-hypoelliptic operators. Already in the case of tori we get an interesting refinement of the classical multiplier theorem.Comment: 22 pages; minor correction

Elements of Potential Theory on Carnot Groups

We propose and study elements of potential theory for the sub-Laplacian on homogeneous Carnot groups. In particular, we show the continuity of the single-layer potential and establish Plemelj-type jump relations for the double-layer potential. As a consequence, we derive a formula for the trace on smooth surfaces of the Newton potential for the sub-Laplacian. Using this, we construct a sub-Laplacian version of Kac’s boundary value problem

Assessing mNIS+7Ionis and international neurologists' proficiency in a familial amyloidotic polyneuropathy trial

INTRODUCTION: Polyneuropathy signs (Neuropathy Impairment Score, NIS), neurophysiologic tests (m+7Ionis ), disability, and health scores were assessed in baseline evaluations of 100 patients entered into an oligonucleotide familial amyloidotic polyneuropathy (FAP) trial. METHODS: We assessed: (1) Proficiency of grading neurologic signs and correlation with neurophysiologic tests, and (2) clinometric performance of modified NIS+7 neurophysiologic tests (mNIS+7Ionis ) and its subscores and correlation with disability and health scores. RESULTS: The mNIS+7Ionis sensitively detected, characterized, and broadly scaled diverse polyneuropathy impairments. Polyneuropathy signs (NIS and subscores) correlated with neurophysiology tests, disability, and health scores. Smart Somatotopic Quantitative Sensation Testing of heat as pain 5 provided a needed measure of small fiber involvement not adequately assessed by other tests. CONCLUSIONS: Specially trained neurologists accurately assessed neuropathy signs as compared to referenced neurophysiologic tests. The score, mNIS+7Ionis , broadly detected, characterized, and scaled polyneuropathy abnormality in FAP, which correlated with disability and health scores. Muscle Nerve 56: 901-911, 2017

Modulation spaces and nonlinear evolution equations

We survey some recent progress on modulation spaces and the well-posedness results for a class of nonlinear evolution equations by using the frequency-uniform localization techniques.Comment: to appear in Evolution Equations of Hyperbolic and Schr\"odinger Type, Progress in Mathematics, Vol.301, Springer, 201