Sentence examples for be a smooth differential from inspiring English sources

Let be a smooth differential form satisfying the nonhomogeneous -harmonic equation in, and.

Let be a smooth differential form satisfying (1.10) in a domain,, and.

Let and,,, be a smooth differential form in a bounded and convex domain.

Let,,, be a smooth differential form in a bounded, convex domain, be the projection operator and be the homotopy operator.

Let,,, be a smooth differential form in a bounded domain, the sharp maximal operator defined in (1.18), and the Green's operator.

Let,, be a smooth differential form satisfying the -harmonic equation (1.10), Green's operator, and the sharp maximal operator defined in (1.18).

Corollary 2.6 Suppose that u is a smooth differential form, φ ( t ) = t p log α ( e + t ), 1 < p < ∞.

Corollary 4.3 Suppose that u is a smooth differential form, φ is a Young function satisfying (2) and q ( n − p ) < n p, 1 < p ≤ q < ∞.

Assume that is a smooth differential form in such that for any real number and, where is a Radon measure defined by for a weight.

Next, we prove the estimate for homotopy operator T. Theorem 4.1 Suppose that u is a smooth differential form, φ is a Young function satisfying (2) with q ( n − p ) < n p, 1 < p ≤ q < ∞.

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