Non-thermal emission in High Frequency Peaked blazars towards the Square Kilometer Array era

In this thesis work we will explore and discuss the properties of the gamma-ray sources included in the first Fermi-LAT catalog of sources above 10 GeV (1FHL), by considering both blazars and the non negligible fraction of still unassociated gamma-ray sources (UGS, 13%). We perform a statistical analysis of a complete sample of hard gamma-ray sources, included in the 1FHL catalog, mostly composed of HSP blazars, and we present new VLBI observations of the faintest members of the sample. The new VLBI data, complemented by an extensive search of the archives for brighter sources, are essential to gather a sample as large as possible for the assessment of the significance of the correlation between radio and very high energy (E>100 GeV) emission bands. After the characterization of the statistical properties of HSP blazars and UGS, we use a complementary approach, by focusing on an intensive multi-frequency observing VLBI and gamma-ray campaign carried out for one of the most remarkable and closest HSP blazar Markarian 421.