Schwartz spaces associated with some non-differential convolution operators on homogeneous groups
Jacek Dziubański (1992)
Colloquium Mathematicae
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Jacek Dziubański (1992)
Colloquium Mathematicae
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Shiying Zhao (1996)
Colloquium Mathematicae
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In this paper, we discuss a class of weighted inequalities for operators of potential type on homogeneous spaces. We give sufficient conditions for the weak and strong type weighted inequalities sup_{λ>0} λ|{x ∈ X : |T(fdσ)(x)|>λ }|_{ω}^{1/q} ≤ C (∫_{X} |f|^{p}dσ)^{1/p} and (∫_{X} |T(fdσ)|^{q}dω )^{1/q} ≤ C (∫_X |f|^{p}dσ )^{1/p} in the cases of 0 < q < p ≤ ∞ and 1 ≤ q < p < ∞, respectively, where T is an operator of potential type, and ω and σ are Borel measures on...
Jacek Dziubański (1993)
Colloquium Mathematicae
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Tang, Canqin, Li, Qingguo, Ma, Bolin (2006)
Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]
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Jacek Dziubański, Jacek Zienkiewicz (1993)
Colloquium Mathematicae
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Nils Dencker (2003)
Journées équations aux dérivées partielles
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We prove the Nirenberg-Treves conjecture : that for principal type pseudo-differential operators local solvability is equivalent to condition (). This condition rules out certain sign changes of the imaginary part of the principal symbol along the bicharacteristics of the real part. We obtain local solvability by proving a localizable estimate for the adjoint operator with a loss of two derivatives (compared with the elliptic case). The proof involves a new metric in the Weyl (or Beals-Fefferman)...
Song Li (1996)
Colloquium Mathematicae
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Edmunds, D.E., Kokilashvili, V., Meskhi, A. (2001)
Georgian Mathematical Journal
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Alimohammady, M., Shahmari, A. (2009)
The Journal of Nonlinear Sciences and its Applications
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