Square functions for wavelet type systems

• Autorzy: Gevorkjan G. , Wolnik B.
• Języki publikacji: EN

Abstrakty

EN

We show the equivalence of the L[sub p] (0 < p [a is less than or equal to] 2) (quasi)-norms of square functions for the systems {2 [...], where f satisfies some decay condition. This implies the boundedness of the shift operator on the wavelet type unconditional basis on L[sub p], 1 < p < [infinity]. We prove also that such operator is unbounded on L[sub 1].

Słowa kluczowe

EN

Haar system; Lp space; regular wavetet; shift operator; square function

PL

falka; teoria operatora; układ Haara

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 1998
• Tom: Vol. 46, no. 2
• Strony: 155--171
• Opis fizyczny: Bibliogr. 12 poz.,

Twórcy

autor

Gevorkjan G.

• Yerevan State University, Alex Manoukian 1, Yerevan 375049, Armenia (GGG)

autor

Wolnik B.

• Institute of Mathematics, Gdańsk University, Wita Stwosza 57, 80-952 Gdańsk, Poland

Bibliografia

• [1] Z. Ciesielski, S. Kwapień, Borne properties of the Наат, Walsh-Paley, Franklin and the bounded polygonal orthonormal bases in LP spaces, Commentat. Math. Tom. Spec. Honor. Ladislae Orlicz. Part 2, Warszawa 1979, 37-42.
• [2] Z. Ciesielski, P. Simon, P. Sjölin, Equivalence of Haar and Franklin bases in LP spaces, Studia Math., 60 (1977) 195-210.
• [3] G. G. Gevorkian, On Haar and Franklin series with the same coefficients, Yerevan Univ. Sci. Notes, 3 (1989) 3-9 (in Russian).
• [4] G. G. Gevorkian, Unboundedness of the shift operator in the Franklin system in the space L1 (in Russian), Mat. Zametki, 38 (1985) 523-533, english transl. in Math. Notes, 38 (1985).
• [5] G. Gripenberg, Wavelet bases in LP(Рг), Studia Math., 106 (2) (1993) 175-187.
• [6] Y. Meyer, Wavelets and operators, Cambrige University Press, Cambrige.
• [7] Y. Meyer, Ondelettes et operateurs II, Opérateurs de Calderón-Zygmund, Hermann, Editeurs des Sciences et des Arts, Paris 1990.
• [8] P. S. Sjölin, J.-0. Strömberg, Basis properties of Наrdу spaces, Arkiv för Mat. 21 (1983) 111-125
• [9] J.-0. Strömberg, A modified Franklin system and highier-order spline systems on Rn as unconditional bases for Hardy spaces, in Conference in harmonic analysis in honor of A. Zygmund, vol. II, Wadsworth, Belmont (1983) 475-494.
• [10] G. G. Walter, Wavelets and other orthogonal systems with applications, CRC Press, Bоса Raton 1994.
• [11] P. Wojtaszczyk, Wavelets as unconditional bases in Lp(R), to be published.
• [12] P. Wojtaszczyk, A mathematical introduction to wavelets, Cambrige University Press, Cambrige 1997.