Sentence examples for complex measurable from inspiring English sources

Throughout this paper, all the processes involved are complex, measurable and of second-order.

As CSF % susA β is influenced by AD-related and AD-unrelated factors, we propose that apparent susA β is a much more complex measure than total measurable CSF A β42 and does not directly represent the total A β42 abundance.

We study the heat kernels of second order elliptic operators in divergence form with complex bounded measurable coefficients on Rn.

Let L be the divergence form elliptic operator with complex bounded measurable coefficients, ω the positive concave function on (0,∞) of strictly critical lower type pω∈ 0,1] and ρ(t)="t−1/ω−1(t−1) for t∈ 0,∞).

In the main part of this paper, the authors develop a theory of Hardy space associated with L, where L is a higher order divergence form elliptic operator with complex bounded measurable coefficients.

We consider complex-valued measurable functions f defined on a measure space ( X, μ ).

Let X and Y be two measure spaces with σ-finite measures μ and ν, respectively, and let f be a complex-valued measurable function on ( X × Y, μ × ν ), 1 < P = ( p 1, p 2 ) < ∞, and 1 ≤ Q = ( q 1, q 2 ) ≤ ∞.

We prove maximal regularity of type Lp Lq for operators in non-divergence form with complex-valued measurable coefficients on Rn.

Let f be a complex-valued measurable function on R n.

Let (mathcal{M}) be the set of all complex-valued measurable functions defined on (mathbb{R}^{n}), and X a linear subspace of (mathcal{M}).

The weighted variable exponent Lebesgue space (L^{p cdot)}(w)) is the set of all complex-valued measurable functions f such that (fw^{1/p cdot)}in L^{p cdot)}(mathbb {R}^{n})).