Inclusions and Noninclusion of Spaces of Convolution Operators

DOI10.2307/1997542zbMath0331.43007OpenAlexW4253108665MaRDI QIDQ4097697

John J. F. Fournier, Michael G. Cowling

Publication date: 1976

Full work available at URL: https://doi.org/10.2307/1997542

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Homomorphisms and multipliers of function spaces on groups, semigroups, etc. (43A22) Fourier series and coefficients in several variables (42B05) Multipliers in one variable harmonic analysis (42A45) (L^p)-spaces and other function spaces on groups, semigroups, etc. (43A15)

Related Items

Translation invariant maps on function spaces over locally compact groups, Universal \(L^p\) improving for averages along polynomial curves in low dimensions, Some sufficient conditions for uniform convergence of Fourier series, Optimal extension of Fourier multiplier operators in \(L^p(G)\), Multipliers in \(H^ p(R^ n)\), \(0<p<\infty\), Group algebras acting on \(L^p\)-spaces, Spaces of Lorentz Multipliers, Convolution-continuous bilinear operators acting on Hilbert spaces of integrable functions, New results on restriction of Fourier multipliers, Some applications of Grothendieck's theory of topological tensor products in harmonic analysis, On the complete bounds of \(L_p\)-Schur multipliers, Unnamed Item, Completely bounded translation invariant operators on \(L^p\), Unnamed Item

Cites Work

• On limits of sequences of operators
• Multiplier transformations of weak type
• Msub(p)(G) non= Msub(q)(G) (psup(-1)+qsup(-1)=1)
• On a class of interpolation spaces
• Pointwise limits for sequences of convolution operators
• Harmonic analysis on \(SL(n,C)\)
• \(L^ p\)-conjecture for locally compact groups. II
• Some inclusions in multipliers
• On L(p,q) spaces
• The multiplier problem
• Bad behavior and inclusion results for multipliers of type (p, q)
• Analytic interpolation of certain multiplier spaces
• Maximal inequalities of weak type
• An indicator diagram for locally compact unimodular groups
• A naively constructive approach to boundedness principles, with applications to harmonic analysis
• Applications of random Fourier series over compact groups to Fourier multipliers
• Harmonic synthesis for subgroups
• \(H^p\) spaces of several variables
• On the Rudin-Shapiro polynomials
• Induced representation of locally compact groups. I
• Left centralizers and isomorphisms of group algebras
• Interpolation of Linear Operators
• Sur la racine carrée du noyau de Poisson dans les espaces symétriques et une conjecture de E. M. Stein
• $L^p$-convolution operators and tensor products of Banach spaces
• A multilinear interpolation theorem
• Approximation of Multipliers
• Multipliers of 𝑝-integrable functions
• Linear operators which commute with translations. Part I: Representation theorems
• Uniformly Bounded Representations and Harmonic Analysis of the 2 x 2 Real Unimodular Group
• L p -Conjecture for Locally Compact Groups. I
• Uniformly Bounded Representations of SL(2,C)
• Convolution of L² - functions
• Uniformly Bounded Representations of the Lorentz Groups
• Intermediate spaces and interpolation, the complex method
• Remarks on weak type inequalities for operators commuting with translations
• The Theory of p-Spaces with an Application to Convolution Operators
• Rudin-Shapiro sequences on compact groups
• Convolution of L(p, q) Functions
• Shorter Notes: Λ(p) Sets and Sidon Sets
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item