Modified Hardy and Hardy–Littlewood operators and their behaviour in various spaces

We study the behaviour of modified Hardy and Hardy–Littlewood operators in $\mathbf P$-adic Herz and Hölder–Besov spaces and in spaces close to $\mathbf P$-adic Hardy spaces and $\mathrm{BMO}$. We also establish a Titchmarsh-type equation for distributions and obtain an estimate for the multiplicative Fourier transform in $\mathbf P$-adic Hardy spaces.