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Let $U$ be a domain of type $H$ in a Brelot potential theory. A compact $K$ in $U$ is a $G_{δ}$ in $U$ iff $U - K$ has at most countably many components. If $F$ is a relatively closed locally polar subset of $U$ , any $G_{δ}$ in $F$ is a $G_{δ}$ in $U$ . If $V$ is a domain in $U$ , all Borel subsets of $\partial V \cap U$ are Baire even if $\partial V \cap U$ is not metrizable. The known results concerning equivalences between weak thinness, thinness, and strong thinness of a set $A$ at a point $x \notin A$ are extended from the case where ${x}$ is a $G_{δ}$ to the cases in which $A$ meets only countably...

Topologie fine dans les espaces harmoniques

E. Haouala (1992)

Mathematica Bohemica

Topologies fines et compactifications associées à certains espaces de Dirichlet

Denis Feyel, A. de La Pradelle (1977)

Annales de l'institut Fourier

Nous commençons par définir la notion d’espaces $L^{1} (γ)$ où $γ$ est une capacité, ce qui permet d’introduire la notion de mesure d’énergie finie par rapport à $γ$ , et de parler d’espaces de Dirichlet basés sur $γ$ .Soit d’autre part un espace de Dirichlet en ce sens avec potentiels s.c.i. : on étudie les espaces de Dirichlet sur les ouverts fins correspondants à l’aide d’une compactification. On retrouve plus facilement et on généralise les résultats de D. Feyel et A. de La Pradelle, (Lecture Notes).

Topologies semi-vectorielles. Application à l'analyse complexe

Pierre Lelong (1975)

Annales de l'institut Fourier

On définit sur un espace vectoriel $E$ une classe de topologies qui rendent la multiplication continue, mais ne sont pas vectorielles en général. Sur un espace complexe $E$ elles permettent d’obtenir encore les principales propriétés des fonctions plurisousharmoniques. De telles topologies séparées sont localement pseudo-convexes (mais non localement convexes en général) : cette notion intervient dans les extensions données récemment par l’auteur du théorème de Banach-Steinhaus aux familles de polynômes...

Trace inequalities for fractional integrals in grand Lebesgue spaces

Vakhtang Kokilashvili, Alexander Meskhi (2012)

Studia Mathematica

rning the boundedness for fractional maximal and potential operators defined on quasi-metric measure spaces from $L^{p), θ} (X, μ)$ to $L^{q), q θ / p} (X, ν)$ (trace inequality), where 1 < p < q < ∞, θ > 0 and μ satisfies the doubling condition in X. The results are new even for Euclidean spaces. For example, from our general results D. Adams-type necessary and sufficient conditions guaranteeing the trace inequality for fractional maximal functions and potentials defined on so-called s-sets in ℝⁿ follow. Trace inequalities...

Traces of pluriharmonic functions

Paolo de Bartolomeis, Giuseppe Tomassini (1981)

Compositio Mathematica

Traces of pluriharmonic functions on the boundaries of analytic varieties.

N.V. Shcherbina (1993)

Mathematische Zeitschrift

Traduzione in equazioni integrali di un problema analogo al problema biarmonico fondamentale

Bruno Pini (1953)

Rendiconti del Seminario Matematico della Università di Padova

Transfinite diameter on curves, Hankel determinants and the moment problem

Len Bos, Sione Ma'u (2015)

Banach Center Publications

We discuss problems on Hankel determinants and the classical moment problem related to and inspired by certain Vandermonde determinants for polynomial interpolation on (quadratic) algebraic curves in ℂ².

Transformation of Three-Dimensional Regions onto Rectangular Regions by Elliptic Systems.

C.W. Mastin, J.F. Thompson (1977/1978)

Numerische Mathematik

Transformations de Marcel Riesz

J. Horvath (1972/1973)

Séminaire Équations aux dérivées partielles (Polytechnique)

Transition density asymptotics for some diffusion processes with multi-fractal structures.

Barlow, Martin T., Kumagai, Takashi (2001)

Electronic Journal of Probability [electronic only]

Transitions on a noncompact Cantor set and random walks on its defining tree

Jun Kigami (2013)

Annales de l'I.H.P. Probabilités et statistiques

First, noncompact Cantor sets along with their defining trees are introduced as a natural generalization of $p$ -adic numbers. Secondly we construct a class of jump processes on a noncompact Cantor set from given pairs of eigenvalues and measures. At the same time, we have concrete expressions of the associated jump kernels and transition densities. Then we construct intrinsic metrics on noncompact Cantor set to obtain estimates of transition densities and jump kernels under some regularity conditions...

Trudinger's inequality for double phase functionals with variable exponents

Fumi-Yuki Maeda, Yoshihiro Mizuta, Takao Ohno, Tetsu Shimomura (2021)

Czechoslovak Mathematical Journal

Our aim in this paper is to establish Trudinger’s inequality on Musielak-Orlicz-Morrey spaces $L^{Φ, κ} (G)$ under conditions on $Φ$ which are essentially weaker than those considered in a former paper. As an application and example, we show Trudinger’s inequality for double phase functionals $Φ (x, t) = t^{p (x)} + a (x) t^{q (x)}$ , where $p (\cdot)$ and $q (\cdot)$ satisfy log-Hölder conditions and $a (\cdot)$ is nonnegative, bounded and Hölder continuous.

Tusk type conditions and thinness for the parabolic operator of order ...

Miroslav Brzezina (1993)

Manuscripta mathematica

Twistor fibrations giving primitive harmonic maps of finite type.

Pacheco, Rui (2005)

International Journal of Mathematics and Mathematical Sciences

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