Pre-Compactness of Sets and Compactness of Commutators for Riesz Potential in Global Morrey-Type Spaces - Nurzhan Bokayev; Victor Burenkov; Dauren Matin; Aidos Adilkhanov (Mathematics)
In this paper, we establish sufficient conditions for the pre-compactness of sets in the global Morrey-type spaces <semantics>G<msubsup>Mpθw(·)</msubsup></semantics>. Our main result is the compactness of the commutators of the Riesz potential <semantics><mfenced separators="" open="[" close="]">b,Iα</mfenced></semantics> in global Morrey-type spaces from <semantics>G<msubsup>Mp1θ1w1(·)</msubsup></semantics> to <semantics>G<msubsup>Mp2θ2w2(·)</msubsup></semantics>. We also present new sufficient conditions for the commutator <semantics><mfenced separators="" open="[" close="]">b,Iα</mfenced></semantics> to be bounded from <semantics>G<msubsup>Mp1θ1w1(·)</msubsup></semantics> to <semantics>G<msubsup>Mp2θ2w2(·)</msubsup></semantics>. In the proof of the theorem regarding the compactness of the commutator for the Riesz potential, we primarily utilize the boundedness condition for the commutator for the Riesz potential <semantics><mfenced separators="" open="[" close="]">b,Iα</mfenced></semantics> in global Morrey-type spaces <semantics>G<msubsup>Mpθw(·)</msubsup></semantics>, and the sufficient conditions derived from the theorem on pre-compactness of sets in global Morrey-type spaces <semantics>G<msubsup>Mpθw(·)</msubsup></semantics>.