Littlewood–Paley Theory and the Multiplier Theorem

2013 ◽  
pp. 53-78
Author(s):  
Feng Dai ◽  
Yuan Xu
Keyword(s):  
Multiplier Theorem

Applications of Erdélyi-Kober fractional integral for solving time-fractional Tricomi-Keldysh type equation

2020 ◽  
Vol 23 (5) ◽  
pp. 1381-1400 ◽  
Author(s):  
Kangqun Zhang
Keyword(s):  
Differential Equation ◽  
Cauchy Problem ◽  
Integral Operator ◽  
Nonlinear Equations ◽  
Existence And Uniqueness ◽  
Fractional Integral ◽  
Formal Solution ◽  
Type Equation ◽  
Multiplier Theorem ◽  
Problem Of Time

Abstract In this paper we consider Cauchy problem of time-fractional Tricomi-Keldysh type equation. Based on the theory of a Erdélyi-Kober fractional integral operator, the formal solution of the inhomogeneous differential equation involving hyper-Bessel operator is presented with Mittag-Leffler function, then nonlinear equations are considered by applying Gronwall-type inequalities. At last, we establish the existence and uniqueness of L p -solution of time-fractional Tricomi-Keldysh type equation by use of Mikhlin multiplier theorem.

Amenability and Translation Experiments

1983 ◽  
Vol 35 (1) ◽  
pp. 49-58 ◽  
Author(s):  
Alan L. T. Paterson
Keyword(s):  
Present Note ◽  
Locally Compact Group ◽  
Finiteness Condition ◽  
Probability Measures ◽  
Multiplier Theorem ◽  
Bounded Linear ◽  
Discrete Semigroups ◽  
Transition Operators ◽  
Semigroup Version ◽  
Similar Issue

In [11] it is shown that the deficiency of a translation experiment with respect to another on a σ-finite, amenable, locally compact group can be calculated in terms of probability measures on the group. This interesting result, brought to the writer's notice by [1], does not seem to be as wellknown in the theory of amenable groups as it should be. The present note presents a simple proof of the result, removing the σ-finiteness condition and repairing a gap in Torgersen's argument. The main novelty is the use of Wendel's multiplier theorem to replace Torgersen's approach which is based on disintegration of a bounded linear operator from L1(G) into C(G)* for G σ-finite (cf. [5], VI.8.6). The writer claims no particular competence in mathematical statistics, but hopes that the discussion of the above result from the “harmonic analysis” perspective may prove illuminating.We then investigate a similar issue for discrete semigroups. A set of transition operators, which reduce to multipliers in the group case, is introduced, and a semigroup version of Torgersen's theorem is established.

scholarly journals Quaternionic spherical harmonics and a sharp multiplier theorem on quaternionic spheres

2019 ◽  
Vol 294 (3-4) ◽  
pp. 1659-1686
Author(s):  
Julian Ahrens ◽  
Michael G. Cowling ◽  
Alessio Martini ◽  
Detlef Müller
Keyword(s):  
Spherical Harmonics ◽  
Multiplier Theorem

scholarly journals Existence of Solution of Space–Time Fractional Diffusion-Wave Equation in Weighted Sobolev Space

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Kangqun Zhang
Keyword(s):  
Wave Equation ◽  
Sobolev Space ◽  
Fractional Derivatives ◽  
Weighted Sobolev Space ◽  
Fractional Diffusion ◽  
Space Time ◽  
Existence Of Solution ◽  
Multiplier Theorem ◽  
Diffusion Wave ◽  
Loss Of Regularity

In this paper, we consider Cauchy problem of space-time fractional diffusion-wave equation. Applying Laplace transform and Fourier transform, we establish the existence of solution in terms of Mittag-Leffler function and prove its uniqueness in weighted Sobolev space by use of Mikhlin multiplier theorem. The estimate of solution also shows the connections between the loss of regularity and the order of fractional derivatives in space or in time.

A short elementary proof of the Lagrange multiplier theorem

2011 ◽  
Vol 6 (8) ◽  
pp. 1597-1601 ◽  
Author(s):  
Olga Brezhneva ◽  
Alexey A. Tret’yakov ◽  
Stephen E. Wright
Keyword(s):  
Lagrange Multiplier ◽  
Elementary Proof ◽  
Multiplier Theorem ◽  
Lagrange Multiplier Theorem

SPECTRAL MULTIPLIERS ON DISCRETE GROUPS

2001 ◽  
Vol 33 (4) ◽  
pp. 417-424 ◽  
Author(s):  
GEORGIOS K. ALEXOPOULOS
Keyword(s):  
Volume Growth ◽  
Discrete Groups ◽  
Multiplier Theorem ◽  
Spectral Multipliers

The classical Mikhlin–Hörmander multiplier theorem is generalised to the context of discrete groups of polynomial volume growth.

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