Appell polynomial sequences with respect to some differential operators

We present a study of a specific kind of lowering operator, herein called A, which is defined as a finite sum of lowering operators and might he presented by various configurations. We characterize the polynomial sequences fulfilling an Appell relation with respect to A, and considering a concrete cubic decomposition of a simple Appell sequence, we prove that the polynomial component sequences are A-Appell, with A defined as previously, although by a three term sum. Ultimately, we prove the non-existence of orthogonal polynomial sequences which are also A-Appell, when A is the lowering operator Lambda = a(0)D+a(1)Dx + D + a(2) (Dx)(2) D, where a(0), a(1) and a(2) are constants and a(2) not equal 0. The case where a(2) = 0 and al not equal 0 is also naturally recaptured.