Estimates for derivatives of holomorphic functions in pseudoconvex domains

Estimates on the mean growth of $H^p$ functions in convex domains of finite type

“…These results were first proved by Hardy-Littlewood for the case of the unit disc ( [6], p. 87). When D is the unit ball and the strictly pseudoconvex domain, the results were proved by Beatrous-Burbea [2] and Beatrous [1]. The key point is the reproducing kernel with right estimate matching quasimetric on ∂D.…”

Fractional derivatives of pointwise multipliers between holomorphic spaces

“…Assertion (vi) for the case p = q is proved in Theorem 1.3 in [9]. An independent proof for 1 < p < ∞ and 1 ≤ q < ∞ can be found for instance in Corollary 3.4 in [23].…”

Division and extension in weighted Bergman-Sobolev spaces

“…It is well known (see for instante [3], [4]) that One of the main results that we will prove in this work is a result of division in the spaces AP,k(D) .…”

“…. X1 is a differential operator we define its weight by k w(X) = 'vVe recall that for a holornorphic function f on D the j -th covariant differential of f at a point z E D is defined by : the holomorphic jet of order m at the point z E D induced by f. Moreover, if the function f is of class A6,k(D), then it is well known (see [1], [3], [4]) that the function di fz(X1, . .…”

“…the problern of extension and restriction of functions of class A6,k(D) ; has been studied by many authors using different methods . (See for exemple [3], [4], [9]) . The result obtained in this case is…”