Estimates for the Norm of Generalized Maximal Operator on Strong Product of Graphs
Let G=G1×G2×⋯×Gm be the strong product of simple, finite connected graphs, and let ϕ:ℕ⟶0,∞ be an increasing function. We consider the action of generalized maximal operator MGϕ on ℓp spaces. We determine the exact value of ℓp-quasi-norm of MGϕ for the case when G is strong product of complete graphs...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2021-01-01
|
| Series: | Mathematical Problems in Engineering |
| Online Access: | http://dx.doi.org/10.1155/2021/9338269 |
| Summary: | Let G=G1×G2×⋯×Gm be the strong product of simple, finite connected graphs, and let ϕ:ℕ⟶0,∞ be an increasing function. We consider the action of generalized maximal operator MGϕ on ℓp spaces. We determine the exact value of ℓp-quasi-norm of MGϕ for the case when G is strong product of complete graphs, where 0<p≤1. However, lower and upper bounds of ℓp-norm have been determined when 1<p<∞. Finally, we computed the lower and upper bounds of MGϕp when G is strong product of arbitrary graphs, where 0<p≤1. |
|---|---|
| ISSN: | 1563-5147 |