Por Daniel Spector (National Chiao Tung University in Hsinchu, Taiwan).
Abstract: From a harmonic analysis perspective, the Riesz transform, fractional Laplacian, and Riesz potentials are all fundamental objects of study. However, dating to J. Horvath's 1959 paper one can find an additional object which has not drawn so much attention that the speaker has termed the Riesz fractional gradient. In this talk we discuss its definition and give a survey of what is known for its implementation in the calculus of variations, PDEs, and harmonic analysis. Open problems will be mentioned.