Duals of homogeneous weighted sequence Besov spaces and applications

• Autorzy: Huang P.-K. , Wang K.
• Języki publikacji: EN

Abstrakty

EN

In this article, we study the duals of homogeneous weighted sequence Besov spaces b α,q p,w, where the weight w is non-negative and locally integrable. In particular, when 0 < p < 1, we find a type of new sequence spaces which characterize the duals of b α,q p,w. Also, we find the necessary and sufficient conditions for the boundedness of diagonal matrices acting on homogeneous weighted sequence Besov spaces. Using these results, we give some applications to characterize the boundedness of Fourier-Haar multipliers and paraproduct operators. In this situation, we need to require that the weight w is an Ap weight.

Słowa kluczowe

EN

almost diagonal; diagonal; dual; double exponent; Fourier-Haar multiplier; paraproduct operator; sequence space; weight

PL

niemal przekątna; przekątna; podwójny wykładnik; współczynnik Fouriera; współczynnik Haara; przestrzeń ciągu

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2011
• Tom: Vol. 17, nr 2
• Strony: 181--205
• Opis fizyczny: Bibliogr. 22 poz.

Twórcy

autor

Huang P.-K.

autor

Wang K.

• Department of Mathematics, National Dong Hwa University (Meilun Campus), Taiwan,

Bibliografia

• [1] M. Bownik, Atomic and molecular decompositions of anisotropic Besov spaces. Math. Z. 250 (2005), 539-571.
• [2] M. Bownik, Duality and interpolation of anisotropic Triebel-Lizorkin spaces, Math. Z. 259 (2008), 131-169.
• [3] M. Frazier and B. Jawerth, A discrete transform and decomposition of distribution spaces, J. Fund. Anal. 93 (1990), 34-170.
• [4] M. Frazier and S. Roudenko, Matrix-weighted Besov space and conditions of Ap type for 0 < p <_ 1, Indiana Univ. Math. J. 53 (2004), 1225-1254.
• [5] J. Garcia-Cuerva and J. Rubio de Francia, Weighted Norm Inequalities and Related Topics, North-Holland Mathematics Studies 116, North-Holland Publishing Co., Amsterdam, 1985.
• [6] R. Hunt, B. Muckenhoupt and R. Wheeden, Weighted norm inequalities for the conjugate function and Hilbert transform, Trans. Amer. Math. Soc. 176 (1973), 227-251.
• [7] N. H. Katz and M. C. Pereyra, Haar multipliers, paraproducts, and weighted inequalities, in: Analysis of Divergence (Orono, ME, 1997), Applied and Numerical Harmonic Analysis, Birkhauser Boston, Boston, MA, (1999), 145-170.
• [8] P. Lemarie and Y. Meyer, Ondelettes et bases hilbertiennes, Rev. Mat. Iberoam. 2 (1986), 1-18.
• [9] C.-C. Lin and K. Wang, Triebel-Lizorkin spaces of para-accretive type and a Tb theorem, J. Geom. Anal. 19 (2009), 667-694.
• [10] C.-C. Lin and K. Wang, The T1 theorem for Besov spaces, preprint.
• [11] M. Meyer, Une classe d'espaces fonctionnels de type BMO. Application aux integrates singulieres. Ark. Mat. 27 (1989), 305-318.
• [12] Y. Meyer, Wavelets and Operators, Cambridge Studies in Advanced Mathematics 37, Cambridge University Press, Cambridge, 1993.
• [13] F. Nazarov and S. Treil, The hunt for a Bellman function: Applications to estimates for singular integral operators and to other classical problems of harmonic analysis (in Russian), Algebra I Analiz 8 (1996), 32-162; translation in St. Petersburg Math. J. 8(1997), 721-824.
• [14] F. Nazarov, S. Treil and A. Volberg, The Bellman functions and two-weight inequalities for Haar multipliers, J. Amer. Math. Soc. 12 (1999), no. 4, 909-928.
• [15] S. Roudenko, Matrix-weighted Besov spaces. Trans. Amer. Math. Soc. 355 (2002), 273-314.
• [16] S. Roudenko, Duality of matrix-weighted Besov spaces, Studia Math. 160 (2004), 129-156.
• [17] H. Triebel, Theory of Function Spaces, Monographs in Mathematics 78, Birkhauser-Verlag, Basel, 1983.
• [18] I. Verbitsky, Imbedding and multiplier theorems for discrete Littlewood-Paley spaces. Pacific J. Math. 176 (1996), 529-556.
• [19] A. Volberg, Matrix Ap weights via 5-functions, J. Amer. Math. Soc, 10 (1997), 445-466.
• [20] K. Wang, The generalization of paraproducts and the full T1 theorem for Sobolev and Triebel-Lizorkin spaces, J. Math. Anal. Appl. 209 (1997), 317-340.
• [21] K. Wang, The full T1 theorem for certain Triebel-Lizorkin spaces, Math. Nachr. 197 (1999), 103-133.
• [22] A. Youssfi, Regularity properties of commutators and BMO-Triebel-Lizorkin spaces, Ann. Inst. Fourier (Grenoble) 45 (1995), 795-807.