How CORESET and Search space are intitalized?
CORESETO information is provided in MIB in the parameter PDCCHConfigSib1 which is a 8 bit no. First 4 bits will provide the frequency domain detail and the last 4 bits will provide the starting position of the CORESETO in time domain as well as the periodicity of CORESETO.
Other CORESET information can be provided in RRC Reconfiguration message
It is not 100% clear to me on what you exactly mean by ‘initialized’ in this context… the idea / details of CORESET 0 and other coreset can be referred to in following notes :