all $(x,y)\in  {\mathcal X}\times {\mathcal 
Y}$, while we use the Euclidean norm for ${\mathbb{R}}^{n}$. The symbol ${\mathbb{N}}$ denotes the set of natural numbers including $0$. If $(i,j) \in \mathbb{N}^2$, we denote by $\delta_{i,j}$ the Kronecker symbol, defined by setting $\delta_{i,j}=1$ if $i=j$ and $\delta_{i,j}=0$ if $i \neq j$. Let ${\mathbb{D}}\subseteq {\mathbb {R}}^{n}$. Then $\mathrm{cl}{\mathbb{D}}$ denotes the closure of ${\mathbb{D}}$, $\partial{\mathbb{D}}$ denotes the boundary of ${\mathbb{D}}$, and $\nu_{\mathbb{D}}$ denotes the outer unit normal to $\partial \mathbb{D}$, where it is defined. We also set ${\mathbb{D}}^{-}\equiv {\mathbb {R}}^{n}\setminus{\mathrm{cl}}{\mathbb{D}}$. For all $R>0$, $ x\in{\mathbb{R}}^{n}$, $x_{j}$ denotes the $j$-th coordinate of $x$, $| x|$ denotes the Euclidean modulus of $ x$ in ${\mathbb{R}}^{n}$, and ${\mathbb{B}}_{n}( x,R)$ denotes the ball $\{
y\in{\mathbb{R}}^{n}:\, | x- y|<R\}$. Let $\Omega$ be an open subset of ${\mathbb{R}}^{n}$. The space of $m$ times continuously differentiable real-valued functions on $\Omega$ is denoted by $C^{m}(\Omega,{\mathbb{R}})$, or more simply by $C^{m}(\Omega)$. Let $r\in {\mathbb{N}}\setminus\{0\}$. Let $f\in \left(C^{m}(\Omega)\right)^{r}$. The $s$-th component of $f$ is denoted $f_{s}$, and $Df$ denotes the jacobian matrix $\left(\frac{\partial f_s}{\partial
x_l}\right)_{  (s,l)\in \{1,\dots ,r\}\times \{1,\dots ,n\}       }$. For a multi-index $\eta\equiv
(\eta_{1},\dots ,\eta_{n})\in{\mathbb{N}}^{n}$ we also set $|\eta |\equiv
\eta_{1}+\dots +\eta_{n}  $. Then $D^{\eta} f$ denotes $\frac{\partial^{|\eta|}f}{\partial
x_{1}^{\eta_{1}}\dots\partial x_{n}^{\eta_{n}}}$. The subspace of 