Abstract
We introduce grand Lebesgue sequence spaces and study various operators of harmonic analysis in these spaces, e.g., maximal, convolution, Hardy, Hilbert, and fractional operators, among others. Special attention is paid to fractional calculus, including the density of the discrete version of a Lizorkin sequence test space in vanishing grand spaces.
Dedicated to Professor V. Kokilashvili on the occasion of his 80th birthday
Funding statement: The first author was partially supported by Pontificia Universidad Javeriana under the research project with ID PPT: 7272. The second and third authors were partially supported by Grant 18-01-00094-a of Russian Foundation of Basic Research.
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Articles in the same Issue
- Frontmatter
- Approximation in generalized Morrey spaces
- On the Cauchy problem for a generalized nonlinear heat equation
- A new principle for arbitrary meromorphic functions in a given domain
- On some generalized Painlevé and Hayman type equations with meromorphic solutions in a bounded domain
- On measurability of real-valued functions in infinite-dimensional topological vector spaces
- A modular variable Orlicz inequality for the local maximal operator
- On the Rellich inequality in Lp(·)(a,b)
- On a generalization of Smirnov’s theorem with some applications
- Space quasiconformal mappings and Neumann eigenvalues in fractal type domains
- Necessary and sufficient condition for the boundedness of the Gegenbauer–Riesz potential on Morrey spaces
- Summability on non-rectifiable Jordan curves
- On generalized fractional cosine and sine transforms
- On mixed norm Bergman–Orlicz–Morrey spaces
- Sharp estimates for the gradient of the generalized Poisson integral for a half-space
- Grand Lebesgue sequence spaces
- Generalized fractional integral operators on generalized Orlicz–Morrey spaces of the second kind over non-doubling metric measure spaces
- A note on N. Bary’s one conjecture
Articles in the same Issue
- Frontmatter
- Approximation in generalized Morrey spaces
- On the Cauchy problem for a generalized nonlinear heat equation
- A new principle for arbitrary meromorphic functions in a given domain
- On some generalized Painlevé and Hayman type equations with meromorphic solutions in a bounded domain
- On measurability of real-valued functions in infinite-dimensional topological vector spaces
- A modular variable Orlicz inequality for the local maximal operator
- On the Rellich inequality in Lp(·)(a,b)
- On a generalization of Smirnov’s theorem with some applications
- Space quasiconformal mappings and Neumann eigenvalues in fractal type domains
- Necessary and sufficient condition for the boundedness of the Gegenbauer–Riesz potential on Morrey spaces
- Summability on non-rectifiable Jordan curves
- On generalized fractional cosine and sine transforms
- On mixed norm Bergman–Orlicz–Morrey spaces
- Sharp estimates for the gradient of the generalized Poisson integral for a half-space
- Grand Lebesgue sequence spaces
- Generalized fractional integral operators on generalized Orlicz–Morrey spaces of the second kind over non-doubling metric measure spaces
- A note on N. Bary’s one conjecture