Martingale operators and Hardy spaces generated by them

• Autorzy: Ferenc Weisz
• Języki publikacji: EN

Abstrakty

EN

Martingale Hardy spaces and BMO spaces generated by an operator T are investigated. An atomic decomposition of the space $H_{p}^{T}$ is given if the operator T is predictable. We generalize the John-Nirenberg theorem, namely, we prove that the $BMO_q$ spaces generated by an operator T are all equivalent. The sharp operator is also considered and it is verified that the $L_p$ norm of the sharp operator is equivalent to the $H_{p}^{T}$ norm. The interpolation spaces between the Hardy and BMO spaces are identified by the real method. Martingale inequalities between Hardy spaces generated by two different operators are considered. In particular, we obtain inequalities for the maximal function, for the q-variation and for the conditional q-variation. The duals of the Hardy spaces generated by these special operators are characterized.

Kategorie tematyczne

• 46E30: Spaces of measurable functions ( L p -spaces, Orlicz spaces, K\"othe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
• 46B70: Interpolation between normed linear spaces
• 60G42: Martingales with discrete parameter
• 60G46: Martingales and classical analysis
• 42B30: H p -spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1995
• Tom: 114
• Numer: 1
• Strony: 39-70

Daty

wydano

1995

otrzymano

1994-02-07

poprawiono

1994-11-07

Twórcy

autor

Ferenc Weisz

• Department of Numerical Analysis, Eötvös Lorand University, Múzeum krt. 6-8, H-1088 Budapest, Hungary.

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