eLpNormLESNormFDerivOfLeConst — Mathlib

English

For a finite-dimensional codomain F and a Haar measure μ on E, the eLp-norm of a function u is bounded above by the product of the constant eLpNormLESNormFDerivOfEqInnerConst(F, μ, p) and the eLp-norm of its derivative: ||u||p' ≤ C(F,μ,p) · ||fderiv u||p.

Русский

Для конечномерного кода F и меры Хаара μ на E, норма eLp функции u удовлетворяет: ||u||p′ ≤ C(F,μ,p) · ||fderiv u||p.

LaTeX

$$$$ \\|u\\|_{p'} \\le C_{F,\\mu,p} \\cdot \\|fderiv\\,u\\|_{p}. $$$$

Lean4

/-- The constant factor occurring in the conclusion of `eLpNorm_le_eLpNorm_fderiv_of_le`.
It only depends on `F`, `μ`, `s`, `p` and `q`. -/
def eLpNormLESNormFDerivOfLeConst :=
  val_proj @wrapped✝.{}

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