The Growth Rate of Harmonic Functions in the Fock Spaces

We establish the pointwise estimate for the arbitrary harmonic function which belongs to the space \(L^{p}(\mathbb {R}^{n},d\mu _{\alpha }),\) $L^p({\mathbb{R}}^n,d{\mu }_{\alpha }),$ \(p>0,\) $p>0,$ where \(d\mu _{\alpha }\) $d{\mu }_{\alpha }$ is the Gaussian measure on \(\mathbb {R}^{n},\) ${\mathbb{R}}^n,$ \(n>2.\) $n>2.$ Also, some norm estimates of the harmonic Fock kernel are included.