Sentence examples for be the potential operator from inspiring English sources

Let P be the potential operator in (1.7) with K ( x, y ) = ϕ ε ( x − y ).

Let,,, be a differential form defined in a domain and be the potential operator defined in (1.4) with the kernel satisfying condition of standard estimates.

Corollary 3.7 Let φ ( t ) = t p, p ≥ 1, let T be the homotopy operator defined in (1.6) and P be the potential operator defined in (1.13).

Let be the potential operator defined in (1.4) with the kernel satisfying the condition of the standard estimates and let be a differential form in a domain.

Let,,, be the solution of the nonhomogeneous A-harmonic equation in a domain and let be the potential operator defined in (1.4) with the kernel satisfying condition of standard estimates.

Let,,, be a differential form defined in a domain, be the Hardy-Littlewood maximal operator defined in (1.9),, and let be the potential operator with the kernel satisfying condition of standard estimates.

Assume that and is the potential operator with for any.

Assume that is the potential operator defined in (1.5) and is a functional satisfying (1.7) and (1.8).

Assume that is the potential operator defined in (1.5) and that is a functional satisfying (1.7) and (1.8).

Assume that and is the potential operator with for any, then there exists a constant, independent of, such that (21).

In this paper, we always assume that P is the potential operator defined in (1.13) with the kernel K ( x, y ) satisfying condition (i) of the standard estimates.