Convolution Algebraic Structures Defined by Hardy-Type Operators

Table 1

Func.\cond.	(HC)𝑝	(𝑑HC)𝑝	(DC)	(DIC)	(AMC)𝑝
𝑗𝛼	𝑝>1	𝑝≥1	✓	✓	𝑝>1
𝜒(0,1)	𝑝>1	𝑝≥1	✓	✓	𝑝>1
𝑒−𝜆	×	×	✓	✓	𝑝>1
𝑒𝜆	×	×	×	✓	×
𝜒(1,∞)	×	×	×	×	×

for 𝛼,𝜆>0.