# Tagged Questions

**1**

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**1**answer

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### Is the fractional integral of order 1/2 of an L_2 function continuous

Let $R_\alpha f(t) = \int_0^t (t-s)^{-\alpha} f(s)\,ds$ the fractional integration operator. If $f \in L_q(0,1)$ for some $q>2$ then $R_{1/2} f$ is (even HÃ¶lder) continuous on $[0,1]$.
My ...

**2**

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**1**answer

366 views

### Fractional integration lemma

Hello everyone.
I am trying to establish a fractional integration lemma of this form.
For $\alpha\geq 0$, and
$1\leq p,q<\infty$ and $0\leq \frac{1}{q}-\frac{1}{p}=\frac{\alpha}{d}$
or $1\leq ...

**3**

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**3**answers

1k views

### Fourier transform of fractional differential operator and Plancherel formula equivalent for fractional norms

I would like to know if the the following exist or are defined
The Fourier transform $\mathcal{F}\left(\frac{d^{\frac{1}{2}}y}{dx^\frac{1}{2}}\right)$ of a fractional differential operator such as ...