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Estimates for the Norm of Generalized Maximal Operator on Strong Product of Graphs
- Source :
- Mathematical Problems in Engineering, Vol 2021 (2021)
- Publication Year :
- 2021
- Publisher :
- Hindawi Limited, 2021.
-
Abstract
- Let G = G 1 × G 2 × ⋯ × G m 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 M G ϕ on ℓ p spaces. We determine the exact value of ℓ p -quasi-norm of M G ϕ for the case when G is strong product of complete graphs, where 0 < p ≤ 1 . However, lower and upper bounds of ℓ p -norm have been determined when 1 < p < ∞ . Finally, we computed the lower and upper bounds of M G ϕ p when G is strong product of arbitrary graphs, where 0 < p ≤ 1 .
- Subjects :
- Article Subject
General Mathematics
010102 general mathematics
MathematicsofComputing_GENERAL
General Engineering
Function (mathematics)
Engineering (General). Civil engineering (General)
01 natural sciences
Action (physics)
010101 applied mathematics
Combinatorics
Strong product of graphs
TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES
Simple (abstract algebra)
Product (mathematics)
QA1-939
Maximal operator
TA1-2040
0101 mathematics
Value (mathematics)
Mathematics
Subjects
Details
- ISSN :
- 15635147 and 1024123X
- Volume :
- 2021
- Database :
- OpenAIRE
- Journal :
- Mathematical Problems in Engineering
- Accession number :
- edsair.doi.dedup.....8149f14897492d39683ec57b88b836e2
- Full Text :
- https://doi.org/10.1155/2021/9338269