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Weighted spaces and a unitary map $L^2(\mathbb R^m) \to L^2([0,\infty) ; L^2(\mathbb S^{m-1}))$

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#fourier-analysis #harmonic-analysis #quantum-mechanics #fractional-sobolev-spaces
134
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Question about the definition of Bessel potentials $H^{s, p}(\mathbb{R}^n)$ and their embeddings

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#fourier-analysis #sobolev-spaces #fractional-sobolev-spaces
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How to think of homogeneous Sobolev spaces

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#partial-differential-equations #fourier-analysis #sobolev-spaces #fractional-sobolev-spaces
76
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Existence of trace operator in$ W^{s,p} (D)$

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#analysis #partial-differential-equations #sobolev-spaces #fractional-sobolev-spaces #trace-map
49
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Elements in fractional Sobolev space

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#sobolev-spaces #regularity-theory-of-pdes #parabolic-pde #fractional-sobolev-spaces
142
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Reference for Sobolev space definition on the boundary

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#partial-differential-equations #sobolev-spaces #fractional-sobolev-spaces
39
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Well definedness of the p fractional Laplace operator

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#integration #analysis #partial-differential-equations #regularity-theory-of-pdes #fractional-sobolev-spaces
150
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Fractional Sobolev space

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#partial-differential-equations #regularity-theory-of-pdes #parabolic-pde #fractional-sobolev-spaces
170
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Trace embedding for derivatives (Sobolev spaces)

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#sobolev-spaces #fractional-sobolev-spaces #trace-map
88
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Fractional powers of a diagonal operator

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#reference-request #operator-theory #hilbert-spaces #semigroup-of-operators #fractional-sobolev-spaces
504
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Inner product of fractional Sobolev space.

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#inner-products #fractional-sobolev-spaces
87
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A question related almost everywhere convergence in Sobolev spaces

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#functional-analysis #partial-differential-equations #sobolev-spaces #regularity-theory-of-pdes #fractional-sobolev-spaces
24
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When is $x \mapsto (1+|x|)^s$ square-integrable?

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#integration #fractional-sobolev-spaces
48
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$H^{\frac{3}{2}-\epsilon}\left(\Omega\right)\hookrightarrow\hookrightarrow H^{1}\left(\Omega\right)$ for $\epsilon\in\left(0,\frac{1}{2}\right)$?

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#sobolev-spaces #fractional-sobolev-spaces
208
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Indicator function and fractional Sobolev spaces

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#fourier-transform #characteristic-functions #fractional-sobolev-spaces

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