Access the full text.
Sign up today, get DeepDyve free for 14 days.
J. Alvarez, J. Hounie (1990)
Estimates for the kernel and continuity properties of pseudo-differential operatorsArkiv för Matematik, 28
Jiangping Xiao, Yin-sheng Jiang, W. Gao (2012)
Bilinear pseudo-differential operators on local hardy spacesActa Mathematica Sinica, English Series, 28
Sagun Chanillo, A. Torchinsky (1985)
Sharp function and weightedLp estimates for a class of pseudo-differential operatorsArkiv för Matematik, 24
J. Tan, Jiman Zhao (2018)
Multilinear pseudo-differential operators on product of Local Hardy spaces with variable exponentsJournal of Pseudo-Differential Operators and Applications, 10
Swastik Kopparty (2018)
Fourier AnalysisAll the Math You Missed
D. Cruz-Uribe, A. Fiorenza (2013)
Variable Lebesgue Spaces
中野 秀五郎 (1950)
Modulared semi-ordered linear spaces
Xi Hu, Jiang Zhou (2018)
Pseudodifferential operators with smooth symbols and their commutators on weighted Morrey spacesJournal of Pseudo-Differential Operators and Applications, 9
Á. Bényi, Diego Maldonado, V. Naibo, R. Torres (2009)
On the Hörmander Classes of Bilinear Pseudodifferential OperatorsIntegral Equations and Operator Theory, 67
J Duoandikoetxea (2000)
Fourier Analysis. Graduate Studies in Mathematics
C Fefferman, EM Stein (1972)
$$H^{p}$$ H p spaces of several variablesActa Math., 129
L. Grafakos, R. Torres (2001)
Discrete decompositions for bilinear operators and almost diagonal conditionsTransactions of the American Mathematical Society, 354
D. Cruz-Uribe, A. Fiorenza (2013)
Variable Lebesgue Spaces: Foundations and Harmonic Analysis
Lin Tang (2010)
Weighted norm inequalities for pseudo-differential operators with smooth symbols and their commutatorsJournal of Functional Analysis, 262
C. Fefferman, C. Fefferman, E. Stein, E. Stein (1972)
Hp spaces of several variablesActa Mathematica, 129
Michael Taylor (1991)
Pseudodifferential Operators and Nonlinear PDE
D. Cruz-Uribe, Sfo, L. Wang (2012)
Variable Hardy SpacesarXiv: Classical Analysis and ODEs
I. Hwang, R. Lee (1994)
^{}-boundedness of pseudo-differential operators of class _{0,0}Transactions of the American Mathematical Society, 346
Á. Bényi, R. Torres (2003)
Symbolic Calculus and the Transposes of Bilinear Pseudodifferential OperatorsCommunications in Partial Differential Equations, 28
O Kováčik, J Rákosník (1991)
On space $$L^{p(x)}$$ L p ( x ) and $$W^{k, p(x)}$$ W k , p ( x )Czchoslov. Math. J., 41
J. Gilbert, A. Nahmod (1999)
Hardy spaces and a Walsh model for bilinear cone operatorsTransactions of the American Mathematical Society, 351
L Tang (2012)
Weight norm inequalities for pseudo-differential with smooth symbols and their commutatorsJ. Funct. Anal., 262
Nicholas Michalowski, David Rule, W. Staubach (2012)
Multilinear pseudodifferential operators beyond Calder\'on-Zygmund theoryarXiv: Classical Analysis and ODEs
David Goldberg (1979)
A local version of real Hardy spacesDuke Mathematical Journal, 46
L. Diening (2005)
Maximal function on Musielak–Orlicz spaces and generalized Lebesgue spacesBulletin Des Sciences Mathematiques, 129
Á. Bényi, R. Torres (2004)
Almost orthogonality and a class of bounded bilinear pseudodifferential operatorsMathematical Research Letters, 11
(1931)
The boundedness of commutator ofmultilinear singular integral operator of Calderón – Zygmund
L Hörmander (1967)
Pseudo-differential operators and hypoelliptic equationsProc. Symp. Pure Math., 10
S Chanillo, A Torchinsky (1986)
Sharp function and weighted $$L^{p}$$ L p estimates for a class of pseudo-differential operatorsArk. Math., 24
J Alvarez, J Hounie (1990)
Estimates for the kernel and continuty properties of pseudo-differential operatorsArk. Math., 28
Lin Yan (2008)
Commutators of pseudo-differential operatorsScience China-mathematics, 51
O. Kováčik, J. Rákosnik (1991)
On spaces $L^{p(x)}$ and $W^{k, p(x)}$Czechoslovak Mathematical Journal, 41
Jodi Herbert, V. Naibo (2013)
Bilinear pseudodifferential operators with symbols in Besov spacesJournal of Pseudo-Differential Operators and Applications, 5
E. Nakai, Y. Sawano (2012)
Hardy spaces with variable exponents and generalized Campanato spacesJournal of Functional Analysis, 262
W. Orlicz (1931)
Über konjugierte ExponentenfolgenStudia Mathematica, 3
IL Hwang, RB Lee (1994)
$$L^{p}$$ L p -boundedness of pseudo-differential operators of class $$S_{0,0}$$ S 0 , 0Trans. Am. Math. Soc., 346
(2012)
Publisher’s Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations
The aim of this paper is to establish the boundedness of the commutator [b , b , T ] 1 2 σ generated by the bilinear pseudo-differential operator T with smooth symbols and b , b ∈ BMO(R ) on product of local Hardy spaces with variable exponents. By 1 2 applying the refined atomic decomposition result, the authors prove that the bilinear p n pseudo-differential operator T is bounded from the Lebesgue space L (R ) into p (·) n p (·) n 1 2 h (R ) × h (R ). Moreover, the boundedness of the commutator [b , b , T ] 1 2 σ on product of local Hardy spaces with variable exponents is also obtained. Keywords Bilinear pseudo-differential operator · Commutator · BMO function · Local Hardy spaces with variable exponent Mathematics Subject Classification 42B20 · 42B35 · 47G30 1 Introduction Hörmander (1967) introduced the class of symbols S with δ, ρ ≥ 0 and m ∈ R, ρ,δ n n composed of a smooth function σ(x,ξ) defined on R × R , such that for all multi- indices α and β, α β m−ρ|α|+δ|α| |D D σ(x,ξ)|≤ C (1 +|ξ |) , (1.1)
Bulletin of the Brazilian Mathematical Society, New Series – Springer Journals
Published: Nov 18, 2019
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.