Generalized and Sharp Trace Gagliardo-Nirenberg-Sobolev Inequalities with Constructive Description of Hardy-Sobolev Spaces

Abstract

We study the functions of bounded mean ascillation area inequality clavceterigation of Bergman spaces in the unit ball of the complex space, Cauchy-type integrals in several complex variables and best constant in Sobolev trace ine qualities on the half-space. We characteribe amass-transportation approach Gagliardo-Niverberg type inequality with lvitical and sharp Sebder inequalities. We obtain the generalized Gagliardo-Niverberg inequalities using weak lebesgue space, Lorentz spaces ltalder spaces and factienal Soboler spaces. The censtructire description of Hardy-Soboler spaces on ctranglyconver demans in the complex spaces with new shap and sharp trace Gagliardo-Niverberg Sahaler ine pqalities for convex cones and improved Borell-Brascomp-lieb inequality are considered.