Abstract
In this paper, the weighted estimates for multilinear pseudo-differential operators were systematically studied in rearrangement invariant Banach and quasi-Banach spaces. These spaces contain the Lebesgue space, the classical Lorentz space and Marcinkiewicz space as typical examples. More precisely, the weighted boundedness and weighted modular estimates, including the weak endpoint case, were established for multilinear pseudo-differential operators and their commutators. As applications, we show that the above results also hold for the multilinear Fourier multipliers, multilinear square functions, and a class of multilinear Calderón–Zygmund operators.
Funding source: National Key Research and Development Program of China
Award Identifier / Grant number: 2020YFA0712900
Funding source: National Natural Science Foundation of China
Award Identifier / Grant number: 12271041
Funding statement: The authors were partly supported by the National Key R&D Program of China (No. 2020YFA0712900) and NNSF of China (No. 12271041).
Acknowledgements
The authors want to express their sincere thanks to the referee for his or her valuable remarks and suggestions, which improve the exposition of the paper.
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Communicated by: Christopher D. Sogge
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© 2024 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Rational points on a class of cubic hypersurfaces
- On fractional inequalities on metric measure spaces with polar decomposition
- Quantitative weighted estimates for the multilinear pseudo-differential operators in function spaces
- The 𝐿𝑝 restriction bounds for Neumann data on surface
- Quasi-triangular, factorizable Leibniz bialgebras and relative Rota–Baxter operators
- Big pure projective modules over commutative noetherian rings: Comparison with the completion
- Any Sasakian structure is approximated by embeddings into spheres
- GIT quotient of holomorphic foliations on ℂℙ2 of degree 2 and quartic plane curves
- The stable category of monomorphisms between (Gorenstein) projective modules with applications
- Gradings and graded linear maps on algebras
- A note on conjugacy of supplements in soluble periodic linear groups
- Discrete Ω-results for the Riemann zeta function
- Is addition definable from multiplication and successor?
- Hausdorff dimension of removable sets for elliptic and canceling homogeneous differential operators in the class of bounded functions
- Statistics of ranks, determinants and characteristic polynomials of rational matrices
- Controllability and diffeomorphism groups on manifolds with boundary
Articles in the same Issue
- Frontmatter
- Rational points on a class of cubic hypersurfaces
- On fractional inequalities on metric measure spaces with polar decomposition
- Quantitative weighted estimates for the multilinear pseudo-differential operators in function spaces
- The 𝐿𝑝 restriction bounds for Neumann data on surface
- Quasi-triangular, factorizable Leibniz bialgebras and relative Rota–Baxter operators
- Big pure projective modules over commutative noetherian rings: Comparison with the completion
- Any Sasakian structure is approximated by embeddings into spheres
- GIT quotient of holomorphic foliations on ℂℙ2 of degree 2 and quartic plane curves
- The stable category of monomorphisms between (Gorenstein) projective modules with applications
- Gradings and graded linear maps on algebras
- A note on conjugacy of supplements in soluble periodic linear groups
- Discrete Ω-results for the Riemann zeta function
- Is addition definable from multiplication and successor?
- Hausdorff dimension of removable sets for elliptic and canceling homogeneous differential operators in the class of bounded functions
- Statistics of ranks, determinants and characteristic polynomials of rational matrices
- Controllability and diffeomorphism groups on manifolds with boundary