Parabolic mean values and maximal estimates for gradients of temperatures

Abstract: We aim to prove inequalities of the form for solutions of on a domain , where is the parabolic distance of to parabolic boundary of Ω, is the one-sided Hardy–Littlewood maximal operator in the time variable on , is a Calderón–Scott type d-dimensional elliptic maximal operator in the space variable on the domain D in , and . As a consequence, when D is a bounded Lipschitz domain, we obtain estimates for the norm of in terms of some mixed norm for the space with denotes the Besov norm in the space variable x and where . [Copyright &y& Elsevier]