Sentence examples for mixed norm estimates from inspiring English sources

As an immediate application, we obtain mixed norm estimates for Π⊗Π in the whole range of Lebesgue exponents.

We establish near-optimal mixed norm estimates for the X-ray transform restricted to polynomial curves with a weight that is a power of the affine arclength.

Additional work is presented in order to extend these mixed norm estimates to the end points, 2n(n + 1) and 2n(n − 1), in the (sharp) form of restricted weak-type inequalities.

New ingredients in our proof include an integration of Timorin's mixed Hodge Riemann bilinear relation and a mixed norm version of Hörmander's L2-estimate, which also implies a non-compact version of the Khovanskiĭ Teissier inequality.

Taking the ℓ 1,2 mixed norm minimization as an example, the matrix V k can be estimated by the following constrained optimization problem [12]: begin{aligned} & underset{boldsymbol{V}}{text{minimize}} & & sum_{i=1}^{L} left|boldsymbol{bar{v}}_{i}right| & text{s.t.} & & |boldsymbol{Y}-boldsymbol{A}boldsymbol{V}|leqvarepsilon.

As a consequence, when D is a bounded Lipschitz domain, we obtain estimates for the Lp norm of δ2n−λ(∇2,1)nu in terms of some mixed norm ∫∞0∥u(⋅,t)∥pBλ,pp(D dt for the space Lp(R+,Bλ,pp(D)) with ∥⋅∥Bλ,pp(D) denotes the Besov norm in the space variable x and where ∇2,1="(∇2,∂∂t).

Hämäläinen, M. S. & Ilmoniemi, R. J. Interpreting magnetic fields of the brain: minimum norm estimates.

Analogously, denotes the Sobolev space with corresponding mixed norm.

In the MMV case the ℓ1-SVD method [7 9] replaces the ℓ1 norm minimization with the mixed norm ℓ2,1 norm minimization.

We endow it with the norm ∥ f ∥ M ( P, Q ) = ∥ V g f ∥ P Q, where ∥ ⋅ ∥ P Q is the norm of the Lorentz mixed norm space.

The boundedness and compactness of the weighted composition operator between mixed norm spaces and are studied.