On the first mixed problem for degenerate parabolic equations in stellar domains with Lyapunov boundary in Banach spaces

The article is devoted to the study of behavior of the solution to a second-order parabolic equation with Tricomi degeneration on the lateral boundary of a cylindrical domain $Q^T$, where $Q$ is a stellar region whose boundary $\partial Q$ is an $(n-1)$ -dimensional closed surface without boundary of class $C^{1+ \lambda}, 0 < \lambda < 1$. We study the question of unique solvability of the first mixed problem for the equation with the boundary andinitial functions belonging to spaces of type $L_p,p > 1$. This topic goes back to the classical works of Littlewood-Paley and F. Riesz devoted to the boundary values of analytic functions. All directions of taking boundary values for uniformly elliptic equations turnout to be equal, and the solution has a property similar to the continuity with respect to a set of variables. In the case of degeneracy of the equation on the boundary of the domain when the directions are not equal, the situation becomes more complicated. In this case, the statement of the rst boundary value problem is determined by the type of degeneracy