We present a complete Lp-theory for such problems which is based on maximal regularity of certain model problems.
We prove that well posedness, that is, maximal regularity of (1.2) in vector-valued spaces, is characterized on Banach spaces having the unconditional martingale difference property ( see, e.g., [4]) by the -boundedness of the set (1.3).
We prove maximal regularity of type Lp Lq for operators in non-divergence form with complex-valued measurable coefficients on Rn.
We prove that the boundedness of a special type of operator valued H∞-calculus is sufficient for maximal regularity of the solution.
shows the maximal regularity of the operator.
In [8] the authors gave a new definition of the Caputo fractional derivative on a bounded interval in the fractional Sobolev space and proved the maximal regularity of solutions of time fractional diffusion equations.
The maximal regularity of this problem in mixed L p norms is derived.
By employing the concept of sums of accretive operators, we shall prove the maximal regularity of problem (1).
Applying Theorem 2.1 we establish the maximal regularity of the problem (3.1) in the mixed norm Z.
In this direction one of the authors in [18] considered maximal regularity for Volterra difference equations with infinite delay.
