Ferenc Weisz

Martingale Hardy spaces and their applications in Fourier analysis

Preliminaries and notations.- One-parameter Martingale Hardy spaces.- Two-Parameter Martingale Hardy spaces.- Tree martingales.- Real interpolation.- Inequalities for Vilenkin-fourier coefficients.

Free lunch and arbitrage possibilities in a financial market model with an insider

We consider financial market models based on Wiener space with two agents on different information levels: a regular agent whose information is contained in the natural filtration of the Wiener process W, and an insider who possesses some extra information from the beginning of the trading interval, given by a random variable L which contains information from the whole time interval. Our main concern are variables L describing the maximum of a pricing rule. Since for such L the conditional laws given by the smaller knowledge of the regular trader up to fixed times are not absolutely continuous with respect to the law of L, this class of examples cannot be treated by means of the enlargement of filtration techniques as applied so far. We therefore use elements of a Malliavin and Ito calculus for measure-valued random variables to give criteria for the preservation of the semimartingale property, the absolute continuity of the conditional laws of L with respect to its law, and the absence of arbitrage. The master example, given by supt[set membership, variant][0,1] Wt, preserves the semimartingale property, but allows for free lunch with vanishing risk quite generally. We deduce conditions on drift and volatility of price processes, under which we can construct explicit arbitrage strategies.

Wiener amalgams and pointwise summability of Fourier transforms and Fourier series

This paper provides a fairly general approach to summability questions for multi-dimensional Fourier transforms. It is based on the use of Wiener amalgam spaces

Ounded Operators on Weak Hardy Spaces and Applications

W(L_p,\ell_q)({\mathbb R}^d)

Some maximal lnequalities with respect to two-parameter dyadic derivative and cesàro summability

, Herz spaces and weighted versions of Feichtingers algebra and covers a wide range of concrete special cases (20 of them are listed at the end of the paper). It is proved that under some conditions the maximal operator of the

(C,α) Summability of Walsh—Fourier Series

\theta

Martingale Hardy spaces and the dyadic derivative

-means

Maximal operator of the Fejér means of triangular partial sums oftwo-dimensional Walsh–Fourier series

\sigma_T^\theta f

Strong Summability of Fourier Transforms at Lebesgue Points and Wiener Amalgam Spaces

can be estimated pointwise by the Hardy–Littlewood maximal function. From this it follows that

The two-parameter dyadic derivative and dyadic Hardy spaces

\sigma_T^\theta f \,{\to}\, f