DLMF:1.14.E45 (Q537)

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DLMF:1.14.E45
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    Statements

    Defining formula
    ∫ - ∞ ∞ | 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,}}
    0 references
    DLMF id
    DLMF:1.14.E45
    0 references
    Symbols used
    Q10895
    Defining formula
    ℋ ⁡ ( f ) ⁡ ( x ) Hilbert-transform 𝑓 𝑥 {\displaystyle{\displaystyle\mathcal{H}\left(\NVar{f}\right)\left(\NVar{x}% \right)}}
    xml-id
    C1.S14.SS5.p1.m2addec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aahdec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aaedec
    0 references
     
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