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103
STOCHASTIC INTEGRATION IN UMD SPACES
"... Building upon previous work by Rosinski and Suchanecki [8] and Brzezniak and the author [1], a systematic theory of stochastic integration for Banach spacevalued functions with respect to Brownian motions has been constructed in [7] using a recent idea of Kalton and Weis to study vectorvalued func ..."
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valued functions through certain operatortheoretic properties of the associated integral operators [4]. In the work presented here, the results of [7] are extended to a theory of stochastic integration for stochastic processes taking values in a UMD space. Let (
n) be a sequence of independent standard Gaussian
equations in UMD spaces and applications
, 2008
"... characterization of periodic solutions for timefractional differential ..."
On the inversion of the Laplace transform for resolvent families in UMD spaces
 THE COMPLEX INVERSION FORMULA REVISITED 9
, 2003
"... Abstract. We analize the inversion of the Laplace transform in UMD spaces for resolvent families associated to an integral Volterra equation of convolution type. 1. ..."
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Cited by 1 (0 self)
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Abstract. We analize the inversion of the Laplace transform in UMD spaces for resolvent families associated to an integral Volterra equation of convolution type. 1.
THE GROUP REDUCTION FOR BOUNDED COSINE FUNCTIONS ON UMD SPACES
, 709
"... Abstract. It is shown that if A generates a bounded cosine operator function on a UMD space X, then i(−A) 1/2 generates a bounded C0group. The proof uses a transference principle for cosine functions. 1. ..."
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Abstract. It is shown that if A generates a bounded cosine operator function on a UMD space X, then i(−A) 1/2 generates a bounded C0group. The proof uses a transference principle for cosine functions. 1.
Periodic Solutions in UMD Spaces for Some Neutral Partial Functional Differential Equations
, 2016
"... Abstract The aim of this work is to study the existence of a periodic solution for some neutral partial functional differential equations. Our approach is based on the Rboundedness of linear operators L p multipliers and UMDspaces. ..."
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Abstract The aim of this work is to study the existence of a periodic solution for some neutral partial functional differential equations. Our approach is based on the Rboundedness of linear operators L p multipliers and UMDspaces.
ON OPERATORVALUED COSINE SEQUENCES ON UMD SPACES
"... A twosided sequence (cn)n∈Z with values in a complex unital Banach algebra is a cosine sequence if it satisfies cn+m + cn−m = 2cncm for any n, m ∈ Z with c0 equal to the unity of the algebra. A cosine sequence (cn)n∈Z is bounded if supn∈Z ‖cn ‖ < ∞. A (bounded) group decomposition for a cosine s ..."
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group decomposition. Here it is shown that if X is a complex UMD Banach space and, with L (X) denoting the algebra of all bounded linear operators on X, if c is an L (X)valued bounded cosine sequence, then the standard group decomposition of c is bounded. 1.
A transference principle for general groups and functional calculus on UMD spaces
 In preparation
, 2006
"... Abstract. Let −iA be the generator of a C0group (U(s)s∈R) on a Banach space X, and ω> θ(U). We prove a transference principle that allows to estimate ‖f(A) ‖ in terms of the Lp(R;X)Fourier multiplier norm of f( · ± iω). If X is a Hilbert space this yields new proofs of important results of McI ..."
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Cited by 8 (5 self)
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Intosh and Boyadzhievde Laubenfels. If X is a UMD space, one obtains a bounded H∞1calculus of A on horizontal strips. Analogous results for sectorial and parabolatype operators follow. Finally we prove that each generator of a cosine function has bounded H∞calculus on sectors. 1.
A NOTE ON UMD SPACES AND TRANSFERENCE IN VECTORVALUED FUNCTION SPACES
, 1999
"... Abstract. A Banach space X is called an HT space if the Hilbert transform is bounded from Lp (X) into Lp (X), where 1 < p < ∞. We introduce the notion of an ACF Banach space, that is, a Banach space X for which we have an abstract M. Riesz Theorem for conjugate functions in Lp (X), 1 < p &l ..."
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Cited by 2 (2 self)
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Abstract. A Banach space X is called an HT space if the Hilbert transform is bounded from Lp (X) into Lp (X), where 1 < p < ∞. We introduce the notion of an ACF Banach space, that is, a Banach space X for which we have an abstract M. Riesz Theorem for conjugate functions in Lp (X), 1 < p
Square functions and spectral multipliers for Bessel operators in UMD spaces, preprint
, 2013
"... Abstract. In this paper we consider square functions (also called LittlewoodPaley gfunctions) associated to Hankel convolutions acting on functions in the Bochner Lebesgue space Lp((0,∞),B), where B is a UMD Banach space. As special cases we study square functions defined by fractional derivative ..."
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Cited by 1 (1 self)
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Abstract. In this paper we consider square functions (also called LittlewoodPaley gfunctions) associated to Hankel convolutions acting on functions in the Bochner Lebesgue space Lp((0,∞),B), where B is a UMD Banach space. As special cases we study square functions defined by frac
Results 1  10
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103