Boundedness of the Generalized Hausdorff Operator on the Cesàro Function Space
Chapter from the book:
Gürbüz,
F.
(ed.)
2024.
Current Approaches in Mathematics and Science.
Synopsis
Banach spaces play an important role in functional analysis and lead to numerous applications, especially since the norms of the spaces are generated by linear operators and p-integrable norms. In this context, the generalized Hausdorff operator has a deep relevance to various problems in analysis. For suitable kernels, the Hausdorff operator is nothing but classical operators such as the Hardy operator, the Cesàro operator, the Riemann-Liouville fractional integral and some other operators. In this work, we investigate the behavior of the generalized Hausdorff operator on the Cesàro function space and determine the conditions φ and a for this operator to be bounded on this space.
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Copyright (c) 2024 Ferit Gürbüz; Kürşat Akbulut, Furkan Yıldırım, İmran Güneş, Ferit Gürbüz, Gülnur Çağlar, Şükrü Canpolat, Elif Yürümez Canpolat, Bülent Karakaş, Şenay Baydaş, Aya Alebo, Çiğdem İnci Kuzu, Kenan Yıldırım