Abstract
In this paper, we introduce new metric characteristics in the space of summable functions. Using these metric characteristics it is obtained Zigmund-type inequalities for the bisingular integral. It is constructed an invariant $T_p$ space for bisingular integral operator according to the inequality. Furthermore, the existence and uniqueness of the solution to the nonlinear bisingular integral equation within the invariant space $T_p$ are proven using the method of successive approximations.
Key words: Bisingular integral operator, Zygmund type estimate, invariant space, summable functions.
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Article Information
| Title | Bisingular Integral with Summable Density |
| Source | Methods Funct. Anal. Topology, Vol. 31 (2025), no. 3, 153-160 |
| DOI | 10.31392/MFAT-npu26_3.2025.01 |
| Milestones | Received 11/05/2024; Revised 27/06/2025 |
| Copyright | The Author(s) 2025 (CC BY-SA) |
Authors Information
Tolliboy Absalamov
Department of Mathematics, Samarkand State University, University blv. 15, 140104, Samarkand, Uzbekistan.
Citation Example
Tolliboy Absalamov, Bisingular Integral with Summable Density, Methods Funct. Anal. Topology 31
(2025), no. 3, 153-160.
BibTex
@article {MFAT2121,
AUTHOR = {Tolliboy Absalamov},
TITLE = {Bisingular Integral with Summable Density},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {31},
YEAR = {2025},
NUMBER = {3},
PAGES = {153-160},
ISSN = {1029-3531},
DOI = {10.31392/MFAT-npu26_3.2025.01},
URL = {https://mfat.imath.kiev.ua/article/?id=2121},
}
