Abstract
In this paper we investigate a general multi-dimensional integral operator \(V_{T}\). Under the condition that the kernel function of \(V_{T}\) is in a suitable Herz space, we get several convergence theorems about norm and almost everywhere convergence and convergence at Lebesgue points. The multi-dimensional convergence is investigated over cones and cone-like sets. As special cases we consider three multi-dimensional integral operators, the \(\theta \)-summation of Fourier transforms and Fourier series and the discrete wavelet transforms. The convergence results are formulated for functions from the Wiener amalgam spaces and variable Lebesgue spaces, too.
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This research was supported by the Hungarian Scientific Research Funds (OTKA) No K115804.
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Szarvas, K., Weisz, F. Convergence of multi-dimensional integral operators and applications. Period Math Hung 74, 40–66 (2017). https://doi.org/10.1007/s10998-016-0157-9
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DOI: https://doi.org/10.1007/s10998-016-0157-9
Keywords
- Variable Lebesgue spaces
- Multidimensional integral operators
- Multidimensional \(\theta \)-summation
- Multidimensional discrete wavelet transform