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On s-sets and mutual absolute continuity of measures on homogeneous spaces.

Tord Sjödin — 1997

Manuscripta mathematica

On $L^{p}$ -differentiability and difference properties of functions

Tord Sjödin — 1982

Studia Mathematica

Weighted norm inequalities for Riesz potentials and fractional maximal functions in mixed norm Lebesgue spaces

Tord Sjödin — 1990

Studia Mathematica

On ordinary differentiability of Bessel potentials

Tord Sjödin — 1984

Annales Polonici Mathematici

On almost everywhere differentiability of the metric projection on closed sets in $l^{p} (ℝ^{n})$ , $2 < p < \infty$

Tord Sjödin — 2018

Czechoslovak Mathematical Journal

Let $F$ be a closed subset of $ℝ^{n}$ and let $P (x)$ denote the metric projection (closest point mapping) of $x \in ℝ^{n}$ onto $F$ in $l^{p}$ -norm. A classical result of Asplund states that $P$ is (Fréchet) differentiable almost everywhere (a.e.) in $ℝ^{n}$ in the Euclidean case $p = 2$ . We consider the case $2 < p < \infty$ and prove that the $i$ th component $P_{i} (x)$ of $P (x)$ is differentiable a.e. if $P_{i} (x) \neq x_{i}$ and satisfies Hölder condition of order $1 / (p - 1)$ if $P_{i} (x) = x_{i}$ .

Bernstein’s analyticity theorem for quantum differences

Tord Sjödin — 2007

Czechoslovak Mathematical Journal

We consider real valued functions $f$ defined on a subinterval $I$ of the positive real axis and prove that if all of $f$ ’s quantum differences are nonnegative then $f$ has a power series representation on $I$ . Further, if the quantum differences have fixed sign on $I$ then $f$ is analytic on $I$ .

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Currently displaying 1 – 6 of 6

On s-sets and mutual absolute continuity of measures on homogeneous spaces.

On $L^{p}$ -differentiability and difference properties of functions

Weighted norm inequalities for Riesz potentials and fractional maximal functions in mixed norm Lebesgue spaces

On ordinary differentiability of Bessel potentials

On almost everywhere differentiability of the metric projection on closed sets in $l^{p} (ℝ^{n})$ , $2 < p < \infty$

Bernstein’s analyticity theorem for quantum differences

Advanced Search

Formula preview

Currently displaying 1 – 6 of 6

On s-sets and mutual absolute continuity of measures on homogeneous spaces.

On L p -differentiability and difference properties of functions

Weighted norm inequalities for Riesz potentials and fractional maximal functions in mixed norm Lebesgue spaces

On ordinary differentiability of Bessel potentials

On almost everywhere differentiability of the metric projection on closed sets in l p ( ℝ n ) , 2 < p < ∞

Bernstein’s analyticity theorem for quantum differences

On $L^{p}$ -differentiability and difference properties of functions

On almost everywhere differentiability of the metric projection on closed sets in $l^{p} (ℝ^{n})$ , $2 < p < \infty$