A Carleson-type estimate in Lipschitz type domains for non-negative solutions to Kolmogorov operators

作者：Cinti Chiara^*; Nystrom Kaj; Polidoro Sergio

来源：Annali della Scuola Normale Superiore di Pisa-Classe di Scienze, 2013, 12(2): 439-465.

We prove a Carleson type estimate, in Lipschitz type domains, for non-negative solutions to a class of second order degenerate differential operators of Kolmogorov type of the form %26lt;br%26gt;L = Sigma(m)(i,j=1)a(i,j)(z)partial derivative x(i)x(j) + Sigma(m)(i=1)a(i)(z)partial derivative(xi) + Sigma(N)(i,j=1) b(i,j)x(i)partial derivative(xj) - partial derivative(t), %26lt;br%26gt;where z = (x, t) is an element of RN+1, 1 %26lt;= m %26lt;= N. Our estimate is scale-invariant and generalizes previous results valid for second order uniformly parabolic equations to the class of operators considered.

• 出版日期2013