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Formula:506

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Digital Library of Mathematical Functions ID 1.14.E45

∫ - ∞ ∞ | ℋ ⁡ f ⁡ ( x ) | p ⁢ d x ≤ A p ⁢ ∫ - ∞ ∞ | f ⁢ ( t ) | p ⁢ d t , subscript superscript superscript Hilbert-transform 𝑓 𝑥 𝑝 𝑥 subscript 𝐴 𝑝 subscript superscript superscript 𝑓 𝑡 𝑝 𝑡 {\displaystyle{\displaystyle\int^{\infty}_{-\infty}|\mathcal{H}\mskip-3.0mu f% \mskip 3.0mu \left(x\right)|^{p}\mathrm{d}x\leq A_{p}\int^{\infty}_{-\infty}|f% (t)|^{p}\mathrm{d}t,}}


Constraint(s)

Symbols List

  • ℋ ⁡ ( f ) ⁡ ( x ) Hilbert-transform 𝑓 𝑥 {\displaystyle{\displaystyle\mathcal{H}\left(\NVar{f}\right)\left(\NVar{x}% \right)}} :
  • d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}} : differential of x
  • ∫ {\displaystyle{\displaystyle\int}} : integral
  • A p subscript 𝐴 𝑝 {\displaystyle{\displaystyle A_{p}}} : coefficient
  •  Edit this on Wikidata

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