scholarly journals A maximal theorem for holomorphic semigroups

2005 ◽  
Vol 56 (1) ◽  
pp. 21-30 ◽  
Author(s):  
G. Blower
Keyword(s):  
Holomorphic Semigroups ◽  
Maximal Theorem

Convolution Estimates and Generalized de Leeuw Theorems for Multipliers of Weak Type (1,1)

1995 ◽  
Vol 47 (2) ◽  
pp. 225-245
Author(s):  
Nakhlé Asmar ◽  
Earl Berkson ◽  
T. A. Gillespie
Keyword(s):  
Abelian Group ◽  
Weak Type ◽  
Full Range ◽  
Locally Compact Abelian Group ◽  
Strong Type ◽  
Locally Compact ◽  
Linearization Methods ◽  
Maximal Theorem ◽  
Abstract Setting ◽  
Central Result

AbstractIn the context of a locally compact abelian group, we establish maximal theorem counterparts for weak type (1,1) multipliers of the classical de Leeuw theorems for individual strong multipliers. Special methods are developed to handle the weak type (1,1) estimates involved since standard linearization methods such as Lorentz space duality do not apply to this case. In particular, our central result is a maximal theorem for convolutions with weak type (1,1) multipliers which opens avenues of approximation. These results complete a recent series of papers by the authors which extend the de Leeuw theorems to a full range of strong type and weak type maximal multiplier estimates in the abstract setting.

scholarly journals Subordinate semigroups and order properties

1981 ◽  
Vol 31 (1) ◽  
pp. 59-76 ◽  
Author(s):  
Akitaka Kishimoto ◽  
Derek W. Robinson
Keyword(s):  
Banach Space ◽  
Holomorphic Semigroups ◽  
Irreducibility Criteria

AbstractLet St = exp{−tH}, Tt = exp{−tK}, be C0-semigroups on a Banach space . For appropriate f one can define subordinate semigroups Sft = exp{−tf(H)}, Ttf = exp{−tf(K)}, on and examine order properties of the pairs S, T, and Sf, Tf. If , = Lp(X;dv) we define St≽ Tt ≽ 0 if St − Tt and Tt map non-negative functions into non-negative functions. Then for p fixed in the range 1 > p > ∞ we characterize the functions for which St ≽ Tt ≽ 0 implies Sft ≽ Tft ≽ 0 for each Lp(X;dv) and the converse is true for all Lp(X;dv). Further we give irreducibility criteria for the strict ordering of holomorphic semigroups. This extends earlier results for L2-spaces.

Weighted fully measurable grand Lebesgue spaces and the maximal theorem

2016 ◽  
Vol 65 (1) ◽  
pp. 221-233 ◽  
Author(s):  
Giuseppina Anatriello ◽  
Maria Rosaria Formica
Keyword(s):  
Lebesgue Spaces ◽  
Maximal Theorem ◽  
Grand Lebesgue Spaces
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